I am having trouble with this problem also derivative differentiate f(x)=(3x)^4(x+5)^3 so far I have 4(3x(x+5)^3+3(x+5)(3x) Not quite right. Treat it as d/dx[u(x) + v(x)] = u dv/dx + v du/dx u(x) = (3x)^4 v(x) = (x+5)^3 du/dx = 4(3x))^3
27,067 results
related rates with work shown
this is a relate rates problem in calculus in a right triangle, the hypotenuse is 5 and the vertical side is x and the angle is theta. so if theta increases at a constant rate of 3 radians per minute, at what rate is x increasing in units per minute when x

calculus
1. Which of the following expressions is the definition of the derivative of f(x) = cos(x) at the point (2, cos(2))? 2. Find the derivative of f(x) = x + 2 at the point (1, 3) 3. Find f '(x) for f(x) = 2x3 + 3x2  x + 15. 4. Find all values of x on the

calculus
I have been asked to solve this two different ways. The first way is to use the chain rule and then simplify (which I have already done properly), and the second way is to simplify and then differentiate (not necessarily with the chain rule). I am stuck on

math
For what intervals is g(x) = 1/x2 + 1 concave down? (Enter your answer using interval notation.) For this question I understand that we have to find where the second derivative is negative. So first I found the first derivative and got 2x/x^4+2x^2+1 and

calculus
Find the surface area of the part of the sphere x^2+y^2+z^2=a^2 inside the circular cylinder x^2+y^2=ay (r=a*sin(θ) in polar coordinates), with a>0. First time posting on this website, sorry for the lack of details on my attempts but I am really not sure

Calculus
Follow the steps below for the given function. (Do not use mixed numbers in your answers.) 2x + 5y = 1 Solve the equation for y. y = Differentiate this equation with respect to x. y ' = Complete the steps below to implicitly take the derivative of the

Calculus (Help)
Also I would like to know how to set this problem up in finding the answer: Find the second derivative. y= sqrt(3x+4) Thanks, P.S. I tried taking 3x+4 and squaring it to the 1/2. I thought that might've been the same, then I took the derivative of that and

Math  Derivatives
How would one take the derivative of "f(x)^[g(x)]? Is there a formula I can follow to differentiate functions like that?

Calculus
Hello, I have some calculus homework that I can't seem to get started..at least not on the right track? I have 3 questions 1. integral of [(p^5)*(lnp)dp] I'm using the uvintegral v du formula So first, I'm finding u and I think it's lnp.......so du is 1/p

Plutonium decay
The amount A(gms) of radioactive plutonium remaining in a 20gm sample after t days is given by: A = 20 * (1/2)^t/140 At what rate is the plutonium decaying when t = 2 days. I think you need to find dA/dt and evaluate it at t=2 This should be a fairly

Calculus
Find f'(c) if f(x)=3e^(x+2)+ e^(5) [NOTE:A small algebraic manipulation is needed first to get f(x) into a form so that the derivative can be taken and your answer isn't a # but rather a formula that returns and answer.] attempt at the problem:

Calculus  Tangent Line
Hi, im having problems with the following problem. The main issue is actually starting the problem. Find the two points on the curve y = x^4  2x^2  x that have a common tangent line. First, find the derivative of y(x) so that you know the slope of the

Calc Help
Find the derivative. Express answer in radical notation with no negative exponents. s=4(sqroot t)+(3/t)+2t^5 This reads (4 times the square root of t) plus (3 divided by t) plus 2t to the 5th. Differentiate it one term at a time, using the rule: d/dt(t^n)

Differentiation
Again, that all makes sense. Thank you very much. Thank you very much. I did get the derivative you show, but then divided through by 6 to get at the stationary points. Was that wrong? I'm only looking for a critique please, not answers! given: f(x)= −2x

calculus
Find the first and second derivative  simplify your answer. y=x/4x+1 I solved the first derivative and got 1/(4x+1)^2 Not sure if I did the first derivative right and not sure how to do the second derivative.

Calculus
How do I use the chain rule to find the derivative of square root(1x^2) also, are there any general hints or tips for determining when the chain rule and product or quotient rule should be used?? i'm having trouble discerning when both the chain rule and

CALCULUS HELP
Find the second derivative for the function 5x^3+60x^236x41 and solve the equation F(X)=0 i got to the second derivative but what do we do next to be able to get one of these answers.. F(x) = 5x3+60x2−36x−41 1. derivative of F(x) with respect to x =

Calculus
I finished this problem but I wanted some feedback because I don't know if it's entirely correct. Suppose that functions f and g and their derivatives with respect to x have the following values at x=2. f(x)=8 g(x)=2 f'(x)=1/3 g'(x)=3 Find d/dx of f(g(x))

Calculus
find derivitive of 1/square root of x 1/square root of x = x^(1/2) The derivative is 1/2 x^(3/2) can you keep going on the problem to not have negative exponents? You can also use that the derivative of 1/f(x) is given by: f'(x)/[f(x)]^2 If you take

calculus
I am having trouble with this problem also derivative differentiate f(x)=(3x)^4(x+5)^3 so far I have 4(3x(x+5)^3+3(x+5)(3x) Not quite right. Treat it as d/dx[u(x) + v(x)] = u dv/dx + v du/dx u(x) = (3x)^4 v(x) = (x+5)^3 du/dx = 4(3x))^3 (using the

calc
derivative of (x^3/6)+(1/2x)? i got (x^2/2)(1/2x^2) is that correct? and then wut is the (F'(x))2?...meaning the derivative squred? if you meant (1/2)x^2  1/(2x^2) you are correct I don't think they are looking for the square of the derivative, but

Calc
y=ln(x+1) +ln(x1) find dy/dx I have trouble with this problem since i'm not that familar with finding the derivative when they involve ln. Please show me how to solve this problem. I should have gotten 2x/(x^21) The derivative of ln(x) is 1/x So, you

math
can some one please help me with the following questions as i don't understand them please (a) write down the derivative of each of the functions f(x)=E7x and g(x)=cos(2x) using the product rule differentiate the function k(x)=E7xcos(2x) (b)write down the

Math
Is it possible to differentiate (60x)/1.2? I'm thinking the answer would be 1/0 which is not possible but I just want to make sure. No problem. Just do a little algebra first. f(x)= (60x)/1.2 = 50  (5/6) x The derivative is df/dx = 5/6 How did you get

math
Differentiate the following function, much like problem 14 of section 3.2 (page 152) of your textbook: y = 14 J + N e^t, where J and N are given constants. Enter the derivative here:

calc
y=ln(x+1) +ln(x1) find dy/dx I have trouble with this problem since i'm not that familar with finding the derivative when they involve ln. Please show me how to solve this problem. I should have gotten 2x/(x^21)

Calc
intergral of (x^3 4x + 3)/(2x) dx would this be ln abs(x^34x+3) + C? I don't really understand how to solve this problem. d/dx (tan (x^2)) sec^2(x^2)(2x) would this be the correct answer to find the derivative of tan (x^2)? no, because if you

trigo help!
1. differentiate cos(3/x) 2. differentiate sin(4/x) 3. differentiate 3/{sin(3x+pi)} 4. differentiate pxsin(q/x)where p and q are constants. 5. differentiate xsin(a/x) where a is constant 6. differentiate sec^3(3x^2+1)

Calc 121
Okay, how would you go about finding the area of a curve from 1 to 4, when y=2x+(2/(x^2))?? It's not like the problem I asked before because here, you cannot use substitution. I tried using 2x for u and x^2 for du but it won't simplify into a ln problem or

calc.
I'm having a lot of trouble with this problem: Sketch the graph and show all local extrema and inflections. f(x)= (x^(1/3)) ((x^2)175) I graphed the function on my graphing calculator and found the shape. I also found the first derivative: (7/3)(x^(4/3))

calculus
I am working on this problem and having some trouble. We're supposed to use partial fractions. The problem is: integral of dx / (x^61) . I got the values of A and D, but I am having trouble with the others. Help please!

Calculus> bobpursley
How do you get m=0? from taking the second derivative? does c=1? Can you check my work on how I get the derivative of R=M^2(c/2m/3) NEXT R=1/2(CM^2)1/3(M^3) NEXT dR/dM=CMM^2. I checked in the back, and that was the answer for the first part of the

Calculus
This is a problem we did previously on a test; my answer was marked correct, but I am having trouble getting my answer in the same form that my teacher gave it. The question: Find the derivative of (x/(x+1))^1/2 His answer: ( (x(x+1))^(1/2) ) / (2x(x+1)^2)

Calculus
1. A rectangular box is to be constructed from 2 different materials. The box will have a square base and open top. The material for the bottom costs $4.25/m2. The material for the sides costs $2.5/m2. Find the dimensions of the box with the largest volume

History
Hello, I am doing this History project where we are required to differentiate the violence exerted by the great powers in context of New Imperialism and the First World War. The problem is that I am having trouble finding articles that actually talk about

Calculus
Any help would be much appreciated with the steps involved in each problem given. Thank you. 1) Find derivative if y =cot x + sin x 2) Find derivative if y = (3x+5)^8 3) Find derivative if y = x csc x 4) Find derivative if y = x ã3x + 1 (3x + 1 is under

Chain Rule
Any help would be much appreciated with the steps involved in each problem given. Thank you. 1) Find derivative if y =cot x + sin x 2) Find derivative if y = (3x+5)^8 3) Find derivative if y = x csc x 4) Find derivative if y = x ã3x + 1 (3x + 1 is under

Calc 121
Okay, how would you go about finding the area of a curve from 1 to 4, when y=2x+(2/(x^2))?? It's not like the problem I asked before because here, you cannot use substitution. I tried using 2x for u and x^2 for du but it won't simplify into a ln problem or

Math 141
I am having trouble with this problem. perform the indicated operations and simpily the result as much as possible a) (3x  2) (x^2 + 2x  4 ) the answer i got so far is 3x^3 + 4x^2 16x + 8. Am i done or i have to conitnue to simplify? if so, what do i

Calculus
Any help would be much appreciated with the steps involved in each problem given. Thank you. 1) Find derivative if y =cot x + sin x 2) Find derivative if y = (3x+5)^8 3) Find derivative if y = x csc x 4) Find derivative if y = x /3x + 1 (3x + 1 is under a

Calculus
This is a large problem, sorry for the trouble. if f(x) = sqrt(x^3 + 5x + 121)(x^2 + x + 11) Find fprime/derivative of/at 0 I keep getting 16 which is not one of the multiple choice answers available. My last step is [sqrt(121)(1)] + [{5/sqrt(121)}(11)]

Calc
1. Differentiae each function a) Y=3x^2+5x4 b) F(x) = 6/x3/x^2 c) F(x)=(3x^24x)(x^3+1) 2. Determine the equation of the tangent line to the curve y=2x^21 at the point where x=2 3. Evaluate, rounding to two decimal places, If necessary a) In 5 b) b)

Math differentiation
Can somebody please check these over for me? I really want to know what I did wrong if I made mistakes! Differentiate the following: 1. y = ln [(4x)/(4+x)] Since it's the ln of the entire thing, then I can apply ln a  ln b so, dy/dx = y' = 1/(4x) *(1)

Calculus
R=M^2(c/2m/3) dR/dM=CMM^2 I found the derivative. Now how would I find the vale of M that maximize the derivative dR/dM? set it to zero, and solve for m. You get two solutions. Use the second derivative to see which one is the max. I get M=C. How do I go

Maths  Calculus
Can anyone help with this...I need to find the derivative of the functions below. If possible please show working so I can try and understand? f(t) =3t^4 and g(t)=sin(4t) Then using the Quotient Rule differentiate the function k(t) 3t^4/ sin(4t) (0

Maths  Calculus
Can anyone help with this...I need to find the derivative of the functions below. If possible please show working so I can try and understand? f(t) =3t^4 and g(t)=sin(4t) Then using the Quotient Rule differentiate the function k(t) 3t^4/ sin(4t) (0

MATH
hi i was just wondering if u could help me with this math problem. find dy/dx at the indicated point in two different ways (a)solve for y as a function of x and differentiate (b) differentiate implicity. 1. y^2=3x+1 (5, 4) how do u do this in two ways? im

Calculus
Derivative Differentiate f(x)=(5x4)^2 There are two ways to do this: (1) let u = 5x4, and use the "chain rule", df/dx = df/du * du/dx OR (2) expand the polynomial to f(x) = 25 x^2 40x + 16 and differentialte it termbyterm. You will get the same answer

Calculus
Area of rectangle = xy = xã(4r^2  x^2) Take the derivative. I am having trouble with the algebra.

Calculus
This is going to be pretty hard to show as text since it would be easier for me to post a picture of the question. The question has f(x) = x/4^2  (2x^3)/4^4 + (3x^5)/4^6 + ... . I am trying to find out the value of f(2). There is a hint to differentiate

Precal
Hi, I don't understand this problem also. Find the the relative maximmum and minimum of x^3  6x^2 + 15. I'm supposed to do it using a graphing calculator but I still don't see any "lows" or "highs". Relative max and mins will occur when the derivative is

math
Let f be a real value function and x Î Df then 0 lim ( ) ( ) h f x h f x ® h +  when it exists is called A) The derivative of f at a B) The derivative of f at h C) The derivative of f at x D) The derivative of f at x = h

Calculus
Hi, I'm having trouble using implicit differentiation to determine dy/dx in the form dy/dx = f(x,y) for sin(2x+3y)=3x^3y^2+4 Do I make it sin(2x+3y)3x^3y^2=4 then differentiate to get 2cos(2x+3y)9x^2*2y=0 ? I'm a little lost... Any help appreciated.

Calc
a) y =ln(x1) find dy/dx=? b) y=3 ln x  ln (1/x) where x >0, dy/dx= ? My teacher says the answers are a) (2x)/(x^21) and b) 4/x I am not sure how you find the derivative when they involve ln. Could you please explain to me how to get these answers? I

caculus
find the nth derivative of 2/(x+1) what i have so far is (?)(x+1)^(n1) i having trouble with finding the first number without using factorial. 2^(n1) works for the first few but not after that

Calculus
relative extrema x^42x^2+5 so far I know how to find the derivative which is 4x^32x now I am stuck... Please help Huh? 4x^32x=0 2x(2x^21)=0 and what are the roots? I will give you a hint: one is x=0 The other two are in the second parenthesis. Is it

Calculus
How do I differentiate ln (2X^2  12X + Y^2 10Y) and the second differentiate it? HELP ASAP is much appreciated

math derivative please help
the derivative of 2x^e is zero right or no? do i have to use the log formula 2 x^e is x to the power 2.718.. It is not a constant and therefore the derivative is not zero. Use the formula for the derivative of x to a power that is constant (x^a). The

AP CALCULUS
What is an equation of the line tangent to the graph of f(x)=x2(2x+1)3 at the point where x=1? (that's x squared (2x+1)cubed) I'm having trouble finding the derivative:f'(x)which would be the slope (m).

Calculus
I have two questions, because I'm preparing for a math test on monday. 1. Use the fundamental theorem of calculus to find the derivative: (d/dt) the integral over [0, cos t] of (3/5(u^2))du I have a feeling I will be able to find the derivative easily,

calculus
Find the derivative using the chain rule. f(x) = ((3x7)/(6x+3))^4 f '(x) = let u= 3x7 v= (6x+3)^4 Then d(uv)= u dv + v du du= 3 dv= 4(6x+3)^5 (6) so what's f'(x)? (thanks for your help) Goodness. f'(x) is d(uv) I will be happy to critique your work or

College Calculus 1
We have to find the first and second derivative of f(x)=x^(2/3)(6x)^(1/3) I have the first derivative as being (4x)/(x^(1/3)(6x)^(2/3)) And that I know is right. The second derivative is 8/(x^(4/3)(6x)^(5/3)) I did all the work but I am not getting

calculus
Let f(x) = (x+1)/(x1). Show that there are no vlue of c such that f(2)f(0) =f'(c)(20). Why does this not contradict the Mean Value Theorem? I plugged 2 and 0 into the original problem and got 3 and 1 . Then I found the derivative to be

calc
What is an equation of the line tangent to the graph of f(x)=x2(2x+1)3 at the point where x=1? (that's x squared (2x+1)cubed) I'm having trouble finding the derivative:f'(x)which would be the slope (m). No one has answered this question yet.

Applied Calculus
Find the first and second derivative of the function: x/(7x+10) Using quotient rule. This is part of my homework in the section named "Higher Order Derivatives". I am confused on getting the second derivative, as I found the first derivative to be

calculus
Please help with this. I submitted it below and was asked to clarify by Henry (hope this is clearer and thank you). I need the first derivative of f(x)=4(x+ sqrt (x(8x)).And then the second derivative of this to show by the second derivative test that it

Derivatives Math
Can someone explain how to find the derivative of : 1. y= 5^ãx / x And the second derivative of: y= xe^10x For this question I got up to the first derivative and got this y = e^10x + 10xe^10x but I can't seem to get the correct answer for the second

Calculus
I need to find the second derivative of y=x(x1)^1/2. I found the first derivative is 2x1/2(x1)^1/2, if someone could check, but I am miserably stuck on the second derivative.

calculus
Please help with this. I submitted it below but no one responded. I need the first derivative of f(x)=4(x+ then the square root to include (x(8x)), then close bracket.And then the second derivative of this to show by the second derivative test that it is

Calculus
How would I go about finding the derivative of f(x)=ln(x)(7x2)^3 first=ln(x) second= (7x2)^3 Would I do first times the derivative of the second + second times the derivative of the first? If so, what is the derivative of lnx? I'm confused. Thanks for

Algebra
Solve and graph. I send this problem last night could someone please help me I have trouble with it. x+122 The solution is { x  x< or X > } please help me with this problem.

Math
I need help with this problem: Write an equation that will give the slope of f(x) at every point: f(x)= 4x^217x+5.6. It seems basic but I am having trouble understanding what the problem is asking for.

Math
Hello I am having trouble with a precalculus problem. The problem is lnSin2XCosX1=0 if you could help by listing the steps to solve that would be great! Thanks!

Math
The problem states that "5 to 8 is as 15 to w." I'm having some trouble solving this because I am unsure of what the problem is asking me to do. Some help would be appreciated. Thank you! :)

MathCalculus (check please)
FOr the function f(x)=x^2e^x Find the critical points, increasing decreasing, first and second derivative and concavity I am having trouble finding the concavity >_< First derivative: xe^x(x+2) Second : e^x(x^2+4x+2) Critical points from first derivate:

Math
Differentiate g(x)=(x^3+1)(3x^21) so I use g'(x) X h(x) + g(x) X h'(x) so the derivative of (x^3+1)=3x^2 and (3x^31)=6x So (3x^2)(x^3+1) + (x^3+1)(6x) Is this correct so far. If so this is where I am stuck. I am having trouble simplifing.

Calculus: Differentiation
I am having trouble solving these. Could you explain how to do these 3 questions, step by step? That would be helpful! 1. Differentiate y=sin ^1 (x^2) at x=0.5 . Round to 3 decimal points. 3. Differentiate y= (x^2 +1) tan ^1 (x) at x=1 7. Differentiate

calculus
Differentiate both sides of the double angle identify sin 2x= 2 sin x cos x to determine an identify for cos x. Find the first derivative, second derivative, third fourth, fifth, sixth, seventh and eighth derivative. Use the results to find the twelfth and

math
If cos(3 x)6Ó14 x e^2 y=0, find [ dy/dx] using implicit differentiation. In this problem, you should differentiate both sides of this equation with respect to x. First, using implicit differentiation, differentiate the left side of the equation with

HELP HELP CALCULUS
y=e^(5e^x) differentiate first and second derivative

Derivative
implicitly differentiate f(x) 2xy= y ^2 find second derivative with relevance to x and y. i get y''= xy'  y/ (yx)^2 this is wrong though. can someone please help me. thank you

Calculus
I'm having problems with this one. Can't get the right answer. Differentiate the following using the chain rule. f(x) = squareroot(x^2+1)/(3x+1) I know that I can take the whole thing and put it to the (1/2) and differentiate that then use the quotient

Calc
sinx+x^2y=1 use implicit differentiation to find the second derivative. For the first derivative I got (cos(x)+2xy)/x^2. I have a feeling that is wrong, can someone please help and show steps on how to do this problem. (studying for a midterm).

Driver Education (Check)
How would you recognize the signs of a problem drinker, and what you do to help that person? A: You would recognize the signs of a problem drinker by looking for chances in a person’s behavior or life situation such as loss of initiative, frequent

calculus
please help! having issue with exponent part of problem. I come to 16x^4 but I think it should be 16x^3.i also have complications with finding the domains. find the derivative of the function using the definition of derivative. f(x)=4x^4 f'(x)=? State the

math
Show the functions f= f(z); z=x+iy is nowhere di fferentiable f(z)=cosy i siny how do i do this? heres my idea separate them into u(x,y) and v(x,y) then differentiate them and since the first derivative of u(x,y) and v(x,y) does not equal i can deduce

Calc I
I am having trouble taking the derivative of the following: t(4t^2)^(1/2) I can't decide if you need to use the product rule or not. What I did is used the PR to get (4t)^1/2)*1t^2*(4t1)^(1/2) Is this correct?

AC circuits
_____R____________    +  XC E1 XL    +   E2 ___________________ Z1 = R= 4 ohms

Calculus
Differentiate to find critical numbers and leave function in fully factored form. g(x) = (x^2+1)^5(x^2+2)^6 g'(x) = (x^2+1)^5[6(x^2+2)^5(2x)] + (x^2+2)^6[5(x^2+1)^4(2x)] g'(x) = 2x(x^2+1)^4(x^2+2)^5[6(x^2+2)(2x) + 5(x^2+1)(2x)] g'(x) =

calculus
1. A rocket is fired vertically into the air. Six kilometers away, a telescope tracks the rocket. At a certain moment, the angle between the telescope and the ground is and is increasing at a rate of 0.6 radians per minute. (See the picture. I have defined

Calculus Help STEVE
find y'' by implicit differentiation. 2x^3 + 3y^3 = 8 I got the first derivative as you but the problem was asking for second derivative by implicit diff. this is where i got confused. Thank you!!!

Calculus Please check
Please check my answers and let me know if I did something wrong. Thank you! Find the partial derivative of x, and the partial derivative of y, then the partial derivative of x (1,1), and the partal derivative of y (1,1). f(x,y) = x^4 y^2 x here is what

calculus
Find the local max/min values of f using botht the first and second derivatie test. I can do the first but I am having trouble with the second derivative. f(x)= x/(x^2+4) Help please...Thank you.

calculus
it is assumed that f is differentiable and that w has an absolute maximum at t0 w(t)= f(t)/(c+t) derivative is f'(t)(c+t)f(t)/(c+t)^2 Show that f(t0) = f′(t0)(C + t0). I'm having a bit of trouble in the above question. I keep getting f(t0)=

math
How can the teacher differentiate instruction when teaching number sense or mathematical operations? Please remember differentiate is for all levels (high, medium, low, ESL, and others)

calculus
What's an example of a short problem where either the first or second derivative test can be applied but the first derivative test is easier? What's an example of a short problem where the second derivative test is easier?

Calculus
I think I have the correct answers for the following problems. For anyone who has the time I would appreciate it if you could tell me if I am correct/incorrect. Thank you. 1). Differentiate ã(x)sin x = (2xcosx+sinx)/2ã(x) 2). Differentiate 2t/(4+t^2)

calculus
Please help with this. I need the first derivative of f(x)=4(x+squareroot (x(8x)) and then the second derivative of this to show by the second derivative test that it is a local maximum. This is difficult to put into form here and I hope I have got it

Calc Derivatives
So, I have a bunch of derivative problems for homework and the only resource I have is the textbook, since we don't have notes. I have just started and want to make sure I'm doing them correctly. Our teacher said we do not have to simplify them either, so

Math(Please check. Thank You)
1) solve:e^x(x^24)=0 e^x=0 and then (x+2)(x2) so x=2, 2 2) differentiate: y=ln(6x^2  3x + 1) 1/(6x^2  3x + 1) * 12x3 3) differentiate: y=e^3x+2 3 * e^3x+2 4) evaluate: 2^4x=8 2^4x = 2^3 4x = 3 x=1 so x=1 5) differentiate: x^3 + y^3 6 =0 3x^2