Find the derivative of 5^(x^3+x) I know the answer, it's: 5^(x^3+x)*ln(5)*(3x^2+ 1) I just need some help on how to derive that. What rule is at work here? where did the ln come from?
147,803 results
Calc I
if f(t)=sqrt(4t+1) find f''(2) I got the first derivative to be: 1/2(4t1)^1/2 * 4t^3 and i'm trying to figure out if i need the product rule again to find the second derivative 1t^3(4t1)^3/2 * 4t^3 The answer if 4/27 and I'm not sure how to get that

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

calculus
Find the derivative of the function using the definition of derivative. g(t)= 9/sqrt(t) g'(t)= state the domain of the function and the domain of the derivative (use interval notation)

Calculus
Let f be a twicedifferentiable function defined on the interval 1.2 less than or equal to x less than or equal to 3.2 with f(1)=2. The graph of f', the derivative of f, is shown on the right. The graph of f' crosses the xaxis at x=1 and x=3 and has a

math
For positive a, b, the potential energy, U, of a particle is given by U = b (a^2 over x^2  a over x) for x is greater than 0 a) find the xintercept b) find the asymptotes c)compute the local minimum d) sketch the graph I don't know how to start this

Calculus 12th grade (double check my work please)
1.)Find dy/dx when y= Ln (sinh 2x) my answer >> 2coth 2x. 2.)Find dy/dx when sinh 3y=cos 2x A.2 sin 2x B.2 sin 2x / sinh 3y C.2/3tan (2x/3y) D.2sin2x / 3 cosh 3yz...>> my answer. 2).Find the derivative of y=cos(x^2) with respect to x. A.sin (2x) B.2x

inverse
If f(x)=cosx + 3 how do I find f inverse(1)? Thanks y = cos(x) + 3 the inverse of this is x = cos(y) + 3 solve for y and you have your inverse The cos function only has a range of [1,1], so the range of f(x) is [2,4]. this means f inverse of 1 doesn't

Calculus
Consider a differentiable function f having domain all positive real numbers, and for which it is known that f'(x)=(4x)x^3 for x>0. A. Find the xcoordinate of the critical point of f. Determine whether the point is a relative maximum, a relative

Calculus
If x = t^2 + 1 and y = t^3, then d^2y/dx^2 = I know I can solve for t in terms of x and substitute that into y = t^3 and find the double derivative. I also know that I can take the derivative of x and y then divide dy/dt by dx/dt. Then take the derivative

Calculus
Find the derivative of the function using the definition of a derivative. F(x)=squareroot(13x) Please show work for understanding, thank you! :)

Calculus
Use a symbolic differentiation utility to find the derivative of the function g(x)=xã((x^2)+1). Use the utility to graph the function and is derivative on the same set of coordinate axes. Describe the behavior of the function that corresponds to any

Calculus questions..really need help, please!
1) Find the value of the lim(x>0) ((sin5x/sin2x)(sin3x4x)). I have no idea where to start so if someone could start it off for me it would really help. 2) If f(x) = (2x3)/(5x+4) then what's the inverse of f(x) So I replaced x with y x = (2y3)/(5y3)

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 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?
1. Find dr/d θ for cosrcot θ=e^r θ 2. Find the normal equation to the curve xy +2xy=0 that are parallel to the line 4x  2y = 10. I know for this I'd have to find the derivative of the curve given. If I rearrange the equation it's (y=xy+2x.... y=2..

Calc.
find the derivative of 3x^45x+3/x^4+1 i know that the derivative of the numeratoor would be 12x^35 but i'm not sure if its right since it has a denominator i Know i need to do something to it but not sure if to simplify.

Calculus
Suppose f(x) and g(x) are functions of x differentiable at x = 4. Given that f(4) = 3, f'(4) = 2, g(4) = 6, g'(4) = 5, find the value of each of the following. a. Derivative of f(x) * g(x) My answer: 27 b. Derivative of (f(x))/(g(x)) My answer: 1/12 c.

Math steve? reiny?
1. Let f(x)=x^5 + 2x^3 + x  1 Find f^1(3) and (f^1)'(3)? I have zero idea how to find the inverse of this function at a point 3, and how to take derivative of an inverse. 2.Let f(x)=cosx + 3x Show that f(x) is a differentiable inverse and find f^1(1)

Calc
1. Find values of a,b,c, and d such that g(x) = a(x^3)+b(x^2)+cx+d has a local maximum at (2,4) and a local minimum at (0,0) 2. Need someone to explain this. Graph a function f(x) for which: f(3)=f(5)=0 f'(x)4 f"(x)>0 for all x I know there is concave

Calculus
Given the function: f(x) = x^2 + 1 / x^2  9 a)find y and x intercepts b) find the first derivative c) find any critical values d) find any local(relative) extrema e) find second derivative f) discuss the concavity g) find any inflection points Please show

Calculus prince@18
let the function h(x)= (integrand symbol from 2 to x^2)arctan (t) dt. Find h'(x). This question confused me because i know the derivative of an integral is the original function. I just need help with finding the derivative of that integral. I don't know

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

Calculus  derivatives
Okay, I want to find the derivative of (x^x)^(x^x)... Well, I already went through the process of finding the derivative of just x^x (I used ln to do this). This is what I found... dy/dx = x^x(lnx+1) So now I want to find the derivative of (x^x)^(x^x)

Calculus
Does my answer look correct? Find the derivative. 11, y= (e^3e)(e+5)/6e my work: ((6e)(4e^3 + 15e^2  2e  5)  (6)(e^4 + 5e^3  e^2  5e))/ (6e)^2 Multiplied/divided everything through My answer: (10e^2 + 30e  3)/ 18 I cant follow your work: I assume e

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 c
Let f be a twicedifferentiable function defined on the interval 1.2 less than or equal to x less than or equal to 3.2 with f(1)=2. The graph of f', the derivative of f, is shown on the right. The graph of f' crosses the xaxis at x=1 and x=3 and has a

calculus
Let F(x)= the integral from 0 to 2x of tan(t^2) dt. Use your calculator to find F″(1) By applying the fundamental theorem of calculus, I got the derivative of the integral (F'(x)) to be 2tan(2x^2) When I take the derivative to find F''(x) I get 8x

math
Find the equation of the tangent line to the graph of f(x) = 2x − 6/x + 1 at the point at which x = 0. (Let x be the independent variable and y be the dependent variable.) I got this question wrong. I thought the answer would be y=4x6 I followed the

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

Math
Consider the following where s is in feet and t is in seconds. s(t) = t^3 + 4t^2 + 6t + 4 (a) Find v(t). v(t) = (b) Find a(t). a(t) = (c) Find v(3). (d) Find a(3). v(t) is the first derivative of s(t). a(t) is the second derivative of s(t). I will be happy

12th Grade Calculus
Find d^2y/dx^2 by implicit differentiation. x^(1/3) + y^(1/3) = 4 I know that first you must find the 1st derivative & for y prime I got 1/3x^(2/3) + 1/3y^(2/3) dy/dx = 0 Then for dy/dx I got dy/dx = [1/3x^(2/3)] / [1/3y^(2/3)] I think that from here

calculus
find the second derivative of F(x)=3e^2x(^2) to find the inflection points. I am trying but I don't think I'm finding the first derivative correctly.

calculus
One litre of water at 0 degrees Celsius will have a different volume at higher temperatures. For a temperature 0 ≤ T ≤ 30 (in Celsius) this volume (in litres) is well approximated by the function V = −aT 3 + bT 2 − cT + 1 using the coefficients a =

Calculus
can sumeone plz help me find the derivative of (2x^2  12x 2) / ((x^2 + x  2) ^ 2) thx a lot Use the following rule: derivative of u(x)/v(x) = [v du/dx  u dv/dx]/ v^2 In your case, du/dx = 4x  12; dv/dx = 2 (x^2 + x 2)*(2x +1) v^2 = (x^2 + x  2)^4

Math: partial derivative
z=u(v+w)^(1/2) find ∂^3z/(∂u∂v∂w) what partial derivative am I suppose to be finding exactly? Do I take the derivative of z three times? Please help. Thank you.

math
find derivative using limit definition: f(x) = x  sqrt(x) so f'(x) = lim h>0 [f(x+h)  f(x)]/h but I keep trying to solve by multiplying by the conjugate but I can't figure it out..there's nothing that can be cancelled or anything and I can't get the

Derivative Calculus
I just need my answers checked. 1) Find the derivative. f(x)=3x^5/4  8/9x^9/8 + x^2  9x + 1 Answer: f’(x)= 15/4x^1/4  x ^1/8 + 2x 9 2) Let f(x)= 7x^3  9x. Find f’(5) Answer: f’(x)=21x^29 f’(5)=516 3) Find the given limit by evaluating the

Calculus
Suppose f(x) and g(x) are functions of x differentiable at x = 4. Given that f(4) = 3, f'(4) = 2, g(4) = 6, g'(4) = 4, find the value of each of the following. a. Derivative of f(x) * g(x) My answer: 27 b. Derivative of (f(x))/(g(x)) My answer: 1/12 c.

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.

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> 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

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 (Derivatives)
I understand finding the derivative and there is a simpler way of doing so, however, can someone show you derive at these answers by the DEF'N of Derivatives? Much appreciated! Question 1: Find, from the definition, the derivative, f'(x), for

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

math
Find the derivative of y=3x2(4^x) Here is my attempt: Derivative of 3x is 3 Derivative of 2 is 0 derivative of 4^x is 4^x(ln(4)) Answer: 12^x(ln(4)) Is this correct? If not please explain what I did wrong and what the correct answer is and why. Thanks!

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 AB
I'm trying to find the second derivative of h(x)= x^2 + cos(kx) My answer for h'(x) is 2x  ksin(kx) but I'm not sure if that's right. Then the answer I got for h''(x) was h''(x) = 2  k^2cos(kx) but I'm pretty sure that's wrong based on the graph I was

local min
f(x) = x^4 + ax^2 What is a if f(x) has a local minimum at x=5. How do I justify the answer. The first derivative has to be zero at x = 5. You then check what the second derivative is at x = 5. If it is positive then that's ok. In this case you find that a

Calculus
1.) Find the derivative of tan (sec x). 2.) Find the derivative if 1/x in four ways, using the limit process, power rule, quotient rule and implicit differentiation. 3.) Show that the derivative of sec^1 x is 1/(x*sqrt(x^2 1)). 4. Find the derivative

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

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
Please help. Applying the chain rule, how do I find the derivative of f(x)=In(e^xe^x) (x>0) and then using this answer use the quotient rule to find the second derivative. I cannot do this so any answer greatly appreciated.

Calculus
Find the value of the derivative (if it exists) of f(x) = (x+3)^(4/3) at x=3. So I got (4*(x+3)^(1/3))/3 for the derivative and 0 for the final answer.

Calculus 1
Find the derivative dy/dx for the following. Simplify your answer. y=(ln(x^2))/(x^3) I got (2/x x^33x^2 ln(x^2))/((x^3)^2) for the derivative is that correct? Or no?

Please check my Calculus
1. Find all critical values for f(x)=(9x^2)^⅗ A. 0 B. 3 C. 3,3 D. 3, 0, 3 E. none of these I got D. I found the derivative and solved for critical numbers. 2. Find all intervals on which the graph of f(x)=(x1)/(x+3) is concave upward A. (negative

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
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

maths
How do I find the derivative of ln(ln(1x))? I know that the derivative of ln(ln(x)) would be 1/xlnx. Would the answer be 1/(1x)ln(1x)?

CALC 1
Suppose that h is a function with h'(x) = xe^x. Find all intervals where the function h is concave up. Now, I understand that concavity is determined by the second derivative, so what my question here is, is it just taking the first derivative and then

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

Math  derivative of sinusoidal (check)
a) Find a function y=f(x) that satisfies the differential equation dy/dx = fifth derivative. This is one of the questions in my practice test, I tried the basic equation of the trig function such as f(x)= sin(x) or f(x)=sin(x) however in the fourth

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.

math please help!!
For what values of x is the graph of y = 8e^−x^2 concave down? (Enter your answer using interval notation.) I started by finding the second derivative and factoring and ended up getting 16e^x^2 (2x^21) and I know up till this part that I'm doing the

calculus
f(x) = 6x^2 8x +3 how would I find the most general antiderivative of the function. I also have to check my answer by differentiation. Would I have to find the derivative first? (I got 12x 8) What are the steps to solving a problem like this? No, don't

Calculus
Given the function: f(x) = x^2 + 1 / x^2  9 a)find y and x intercepts b) find the first derivative c) find any critical values d) find any local(relative) extrema e) find second derivative f) discuss the concavity g) find any inflection points Please show

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

calculus
Please help, my live tutor and I could spent 2 hours trying to solve these two: find an equation for tangent line y=18^2@ (4,129) find the derivative of the function:we both kept getting the same answer, but Mathlab kept saying that it was wrong:

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

derivative am i right or wrong
what is the antiderivative of 1/(x^22x+2)? does antiderivative mean find the derivative of the function or integrate it. is the answer ln(x^22x+2) or is2(x^22x+2)^2. These are part of the multiple choices. antiderivative is the integral. so would the

Calculus
Given the function: f(x) = x^2 + 1 / x^2  9 a)find y and x intercepts b) find the first derivative c) find any critical values d) find any local(relative) extrema e) find second derivative Please show me how u got this!!

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

Calculus
An airplane flies at an altitude of 5 miles toward a point directly over an observer. The speed of the plane is 600 mi/hr. Find the rate at which the angle of elevation is changing when the angle is 30 degrees. I found the answer to be 60 radians/hr by

Math
How would you fine the relative extrema of f(x)=x+8^x ? I know the first step is to find the derivative, which when I did I got f'(x)=1+[(1)(ln(8))(8^x)] Did I find the derivative correctly? And if I did, how do I find the zeroes of that??

Calc
Find the derivative of a) y=cos (x/2) b) yx3x^2 +6 = y^4 + x a) sin (x/2)(2+x)/2^2 sin(x/2)(x/2) b) x dy/dx + y  6x = 4y^3 dy/dx + 3x^2 dy/dx (x 4 y^3) = 3x^2 y +6x dy/dx = (3x^2 y +6x)/(x 4 y^3) I used inplicit differation for part b are these

CalculusAB
determine if differentiable everywhere: 3xabs(x)1=y i know you're supposed to find the derivative....  then my mind draws a blank? hahah please help me out also y=x ^ 2/5 you find the derivative and it is 2/(5x^(3/5)) now what? thanks so much

Calculus
How do I use the product rule to solve these two questions. Much appreciated! xo Find the derivative for k(x) = (5x4 + 2)(3sin x) Find the derivative for m(x) = ex cos x at x = 1

Math
find the derivative of x^36x^2+15x+8 and show by completing the square that function has no turning point. I can find derivative but not sure of next step

maths
(a)(i)use the composite rule to differentiate the function f(x)=(x^26x+23)^(3/2). (ii)use the composite rule and your answer to part (a)(i) to show that the function g(x)=(x2)/(x^26x+23)^(3/2) has derivative g'(x)=(5+9x2x^2)/(x^26x+23)^(5/2).

Is this f'(x) or partial derivative?
Find d VC/ d y = ((y/240)^2)(w) = 2yw/240^2 + 0 + y^2/240^2 but final answer is.... = 2yw/240^2 So, is the question asking for partial derivative or first derivative? I think partial because the final answer only took the derivative with respect to y.

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

calc
find the area between the xaxis and the graph of the given function over the given interval: y = sqrt(9x^2) over [3,3] you need to do integration from 3 to 3. First you find the antiderivative when you find the antiderivative you plug in 3 to the

MoRe HeLp PlEaSe!! (calc)
Also can I get some help with this LONG, TIRESOME PROBLEM? Find the derivative using the chain rule. f(x)= ((3x7)/(6x+3))^4 Thanks a lot! (68/(12x^2+12x+3))*[(3x7)/(6x+3)]^3 you should double check the answer multiply 4((3x7)/(6x+3))^3 by the derivative

Calculus
I need help with finding first and second derivativesimplify your answer. Y=xtan(x) I solved first derivative xsec^2(x) + tan(x) I don't understand how to get the first...can someone show me the steps with explanation?

Calculus
Determine whether or not each of the following functions is invertible. Give your reasons for believing the function is invertible or not. Please check this for me. I am not sure if I am adequately explaining my answer and if my answer is right. a) y=

Math
Could I please get some help for these 3 questions, apologies for asking so many, but they were the ones I was really unsure of: 1. Find an equation for the line tangent to y=ln(x) and that goes through the origin. I have no idea, the ln(x) stuff is

Calc Help
Find two functions that this could be the derivative of: y'=4x+7 Remember the derivative of any constant is zero. take its antiderivative i suppose... y= 2x^2 + 7x + any number

maths
f(x)=ln(e^xe^x), x>0 By applying in turn the Composite and Quotient Rules, find derivative and second derivative.

Calculus
If P'(t)= [10(t+2)]/t. What is P(t)? It is asking for the derivative, and I am so lost! Because so far we haven't covered how to find the derivative of something so complicated. Any ideas? TY

maths
f(x)=ln(e^xe^x), x>0 By applying in turn the Composite and Quotient Rules, find derivative and second derivative. Thanks.

maths
f(x)=ln(e^xe^x), x>0 By applying in turn the Composite and Quotient Rules, find derivative and second derivative. Thanks.

maths
f(x)=ln(e^xe^x), x>0 By applying in turn the Composite and Quotient Rules, find derivative and second derivative. Thanks.

Calculus
Use derivative formulas to find the derivative of the function. please show your work h(x)=10^325x^6+3x^15

Math
1. f(x)=x^2(e^x) find a point where the tangent is horizontal. The answer is apparently (2, 4/e^2). But I got 0 when I solved for the derivative. I don't get this. 2. What value of x does the function f(x)=(x^3+27)^(1/2) have vertical tangents? My

calculus
find the derivative of f(x)=x^2sec^2(3x) also with g(x)=sqrt(cosxsecx) i get zero because cos and sec cancel each other out and derivative of a constant is zero... am i doing something wrong?

calc
f(x)= x^3/x^216 defined on [19, 16] How would you find the vertical asymptopes? and the inflection point? I think you take the derivative and set it to zero? but i cant figure out the correct derivative or something??

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

Math
Find the derivative of f(x)= 2 sqrt x at x=4. i thought that the derivative would be 2 x^1/2 but I guess this is wrong.

calculus
i need to use implicit differentiation to find the derivative: yx+y = 8 i keep getting y'=1y. i already know the derivative of this, by using explicit by simplification: y(x+1)=8 y=(8)/(x+1) y'= (8)/(x+1)^2 how do i go about doing this the right way?

Calculus AB
The position function of a particle in rectilinear motion is given by s(t) = 2t^3  21t^2 + 60t + 3 for t ≥ 0. Find the position and acceleration of the particle at the instant when the particle reverses direction. Include units in your answer. So I've