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derivative

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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--> 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/2-m/3) NEXT R=1/2(CM^2)-1/3(M^3) NEXT dR/dM=CM-M^2. I checked in the back, and that was the answer for the first part of the equation. Isn't 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 rather the second ...

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 formula for that may ...

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) (using ln). This is what ...

math
Find the derivative of y=3x-2(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!

Math Derivative
Find derivative of f(x)=g(h(x)) Would the derivative be something like: g'(h(x))*h'(x) ??

Math (Derivative)
Computer the derivative of f(x)=x-(1/x) for x>0 using the definition of the derivative.

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 of 2^(e^(sin x)). ...

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 derivative.

Calculus
R=M^2(c/2-m/3) dR/dM=CM-M^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 from there? What do ...

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

Math (Derivative)
Compute derivative using the definition of the derivative. f(x)=1+1/x^2 1+ 1/(x+h)^2 - (1+ 1/(x^2)) ------ divide by h and multiply by reciprocal 1/h(x+h)^2 - 1/hx^2 Next I expanded it and got this messy huge number and multiply the bottom of each other after cancelling some ...

Calc-please help!
What is the second derivative of (x^3)/(x^2-1)? And how would I accurately graph both the derivative and the second derivative of this function?

CALCULUS HELP
Find the second derivative for the function 5x^3+60x^2-36x-41 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 = 15x2+120x&#...

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 got 1/2(3x+4)^(-1/2...

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 3 +21x 2 −...

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 fifteenth derivative...

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
Please help with this. I need the first derivative of f(x)=4(x+squareroot (x(8-x)) 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 right. Many thanks.

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 the square root) 5...

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 the square root) 5...

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 square root(/) 5) ( f...

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 I got @f/@x = 3x^3 y...

Derivative
Can you help me find the derivative of y= cos(x)/1+sin(x).. the / is a fraction bar. I have a hard time finding trig derivatives because I don't really know what the derivative of cos,sin ,or tan would be honestly.

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. Derivative of (g(x...

Calc I
if f(t)=sqrt(4t+1) find f''(2) I got the first derivative to be: 1/2(4t-1)^-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(4t-1)^-3/2 * 4t^3 The answer if -4/27 and I'm not sure how to get that if I'm doing the ...

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(8-x)).And then the second derivative of this to show by the second derivative test that it is a local maximum. ...

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
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. Derivative of (g(x...

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 10/(7x+10)^2

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 derivative they reach the ...

Math - derivative of a rational function
find the 1st derivative of f(x) = x/(x-1)2 Is the 1st derivative f'(x)= -x-1/(x-1)^3

derivative
Would the first derivative of R(t)=9t[(t-4)^3/2.718] be R'(t)=3.311258278(3(t-4)^2(t)+(t-4)^3) and the second derivative be R''(t)=3.311258278(6(t-4)x+6(t-4)^2)?

Calculus
If I have a function f(x), and am given its derivative, f'(x): may I take it as a given that f(x) is an integral of f'(x). My reasoning is that 'undoing' the derivative gives me the derivative. Eg is 1/3x^3 an integral of x^2? Thanks.

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 then I took the second ...

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(8-x)), then close bracket.And then the second derivative of this to show by the second derivative test that it is a local maximum. This...

math
I have the same project as Jill down there... -What is the definition of a derivative? -What does the derivative of a function tell you (in english) ? Then I need an example of the power rule, quotient rule, and chain rule. -What information does the FIRST derivative tell you ...

Calculus
Use a symbolic differentiation utility to find the derivative of the function g(x)=xã((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 zeroes of the graph of ...

Calculus derivative
find the slope m and an equation of the tangent line to the graph of the function f at the specified point. original: x^2/x+10 point: (3,9/13) After I found the derivative: (x+10)(2x)-(x^2)(1)/((x+10))^2 How do I get the slope? Should I put 3 into the derivative equation?

calculus
Could someone check my reasoning? thanx Find the derivative of the function. sin(sin[sinx]) I need to use the chain rule to solve. So I take the derivative sin(sin[sinx) first. Then multiply that by the inside which is the derivative of sin[sinx]. And multiply that by ...

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 = -50 and that the ...

Calculus
How would I go about finding the derivative of f(x)=ln(x)(7x-2)^3 first=ln(x) second= (7x-2)^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 your help. --Cori

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.

Calculus
Does my answer look correct? Find the derivative. 11, y= (e^3-e)(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 is a derivative. (e^3...

Calculus
Explain the global optimization process for a continuous function over a closed interval. Be sure to identify all steps involved and clearly explain how the derivative is utilized in this process. Does this have to do with the first derivative rule or second derivative rule ...

Calculus
Explain the global optimization process for a continuous function over a closed interval. Be sure to identify all steps involved and clearly explain how the derivative is utilized in this process. Does this have to do with the first derivative rule or second derivative rule ...

Calc
a) y =ln(x-1) 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^2-1) 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 have a quiz on them ...

Calculus derivatives
f(a) = a + √a (a) Find the derivative of the function using the definition of derivative.

Ab Initio Derivative
Can anyone plz post the procedure for finding the derivative of :- e^ax by ab inition method?

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.

Derivative
Evaluate the following: a) S (4x^2+3)/x^2 dx b) S 4x(x^2+3) dx Please help and show the working so that I can understand as I hv no foundation in derivative. TQ

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

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
Calculate the derivative of the function. Then find the value of the derivative as specified. f(x) = 8/(x+2); f '(0)

Calc
Set the first derivative and second derivative of x^2/x-2 equal to 0. Solve for 0.

Math
what value of x is the derivative of x^3 is equal to the derivative of x^2 + x? can someone help me out please

derivative of y
how to find derivative of y: y = sin inverse(square root of 2t) I got this. Please ignore.

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

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

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

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

Calculus I
Find the derivative of y=ln((1+e^x)/(1-e^x)) I know that the derivative of y=ln(1+e^x) would be (e^x)/(1+e^x), but I'm not sure what to do with the 1-e^x on the bottom here. Can someone help please? Thanks!

Calc-Derivative
Find the derivative of x^(1/x). Can someone show me steps for this problem...I go round in circles

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.

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

calculus
Use the function defined below to calculate the indicated derivative. f(t)= 4/(t^3)+3 what is f''(2) (second derivative) Need help!!

Calculus
Use derivative formulas to find the derivative of the function. please show your work h(x)=10^3-25x^6+3x^15

calculus
3. Plot f(x) =ln(x) and f’(x) = 1/x in your calculator. Remembering that the derivative of f(x) is the instantaneous rate of change of f(x) why does it make sense that 1/x is the derivative of ln(x)?

Math
How would I find the derivative of x^2 + 3x using the definition of the derivative?

Derivative
if g(x)= 5x^6-3/x^2, find the 3rd and 5th derivative of the function. Pls help!

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

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^2-9 f’(5)=516 3) Find the given limit by evaluating the derivative. lim h⇒...

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 taking it again? Is it ...

Calculus
Find the derivative of the function using the definition of a derivative. F(x)=squareroot(1-3x) Please show work for understanding, thank you! :)

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

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

Math/Derivative
Can someone help me figure out the answer and..possibly show the steps.. to finding the derivative of these 3 questions.. 1. f(x)=2(e^x) - x^2 2. f(x)=e^x/(e^x +1) 3. y=10^(√x)

Calculus (Global Max)
Explain the global optimization process for a continuous function over a closed interval. Be sure to identify all steps involved and clearly explain how the derivative is utilized in this process. Does this have to do with the first derivative rule or second derivative rule ...

Calculus
Find the derivative of f(x)=x(1-4^x) f'(x)=(1-4^x)+ (-4^x)(ln-4)(-4)(x) ln can't be negative. Is the derivative correct?

Calculus
Find the derivative of m(x)=1/(x+1) by using the definition of the derivative.

Math
By direct use of the definition of a derivative, the derivative of f(x) = 1/x ?

Calculus
Hello I need help with this excersise of derivative of a inverse function. The excersise says: If f(x+2)=x^3+1 and g(x)=f(arctg x), find the derivative of the inverse function of g(x) and then calculate (g^-1 (9))'[the derivative of the inverse function evaluated in 9] . I don...

chemistry
Why is the second derivative of a titration curve more accurate method to determine endpoints and equivalence points than the first derivative?

main legal issues
CATCHWORDS: CORPORATIONS - statutory derivative action - application by 35% shareholder/director to bring derivative proceedings after company's assets were transferred to a company from which the applicant is excluded - inadequacies of proposed points of claim - whether those...

Calculus
Show that the curves r=acos(è) and r=cos(è) intersect at right angles. can it be shown that the derivative of one is the negative reciprocal of the derivative of the other?

Calculus Derivative
I'm trying to calculate the derivative of this: P= mv/ sqrt(1-v^2/c^2)where m and c are constants, and v depends on t. I know about the chain and product rules but I'm not even sure where to start. :/ Thank you for your help.

partial differentiation
u(x,y)=xln(x^2+y^2)-(2y times inverse of tan of y/x) 1)find derivative of u wrt to x and then wrt y 2)show that (x times derivative of u wrt x)+(y times derivative of u wrt y) = u +2x

Calculus,Stationary Points,First derivative test
Good afternoon, I need a bit of help. So ive got my first derivative which is 6x^2-6x-12 and the stationary points ive found are x=-1 and x=2 at which points the value of the derivative is zero. So im attempting to classify the points. From my derivative tests the value of -2 ...

calculus
If the hands on a clocktower's clock are 2ft and 3ft long, how fast is the distance between the tips of the hands of the clock changing at 9:20? I know that the derivative of the minute hand is pi/30 rad/min and derivative of the hour hand is pi/360 rad/min. what is the ...

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 Put it all together

calculus
Hello. I need help finding the open intervals of this equation: f(x)=3x^2-12 I already took the derivative of it by using the derivative test and I got 2,-2 as critical numbers

calculus
Hello. I need help finding the open intervals of this equation: f(x)=3x^2-12 I already took the derivative of it by using the derivative test and I got 2,-2 as critical numbers

calculus
For a function f(x) the derivative at x=2 is 5. Is the derivative of f(x) continuous at x=2? Thanks!

calc
How do you find the derivative of: ln(3x^2 + x - 1) I know the derivative of lnx is 1/x

calculus
Would the derivative of ln(x^2) be 1/x^2? and also the derivative of ln(2^s) be 1/2^s

Calculus derivative
How do you do the derivative of a^x, for example, (3/4)^x Thank you for helping!

calculus derivative HELP!
Find the derivative of: y=2sqrt(x)-(1/x)

Calculus
let F(x) = f(2x) and suppose that the derivative of F(x) = x^(2). Find the derivative of f(2x).

Quantum mechanics, eigenfunctions!
Determine if the function sin(x)*e^(ax) where a=constant is an eigenfunction of the operators d/dx and d^2/(dx)^2 Okay. My understanding is that you use the operator and perform its "thing" on the function. In this case, you will have to find the 1st derivative of sin(x)*e^(ax...

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