calculus

Please help. Applying the chain rule, how do I find the derivative of f(x)=In(e^x-e^-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.

  1. 👍 0
  2. 👎 0
  3. 👁 61
asked by mary
  1. f(x) = ln(e^x - e^-x)

    f'(x) = (e^x + e^-x)/(e^x - e^-x)

    f''(x) = [(e^x - e^-x)(e^x - e^-x) - (e^x + e^-x)(e^x + e^-x)]/(e^x - e^-x)^2
    = [(e^x - e^-x)^2 - (e^x + e^-x)^2]/(e^x - e^-x)^2

    1. 👍 0
    2. 👎 0
    posted by Reiny

Respond to this Question

First Name

Your Response

Similar Questions

  1. MoRe HeLp PlEaSe!! (calc)

    Also can I get some help with this LONG, TIRESOME PROBLEM? Find the derivative using the chain rule. f(x)= ((3x-7)/(6x+3))^4 Thanks a lot! (68/(12x^2+12x+3))*[(3x-7)/(6x+3)]^3 you should double check the answer multiply

    asked by Confused on February 21, 2007
  2. Calculus

    How do I use the chain rule to find the derivative of square root(1-x^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

    asked by Elizabeth on October 7, 2008
  3. Math, Calculus

    Find the derivative of the function. y= xcosx - sinx What's the derivative? I get only one trig function. I will be happy to critique your work or thinking. Use the chain rule on the first term. Our class hasn't covered Chain

    asked by Jonah on March 6, 2007
  4. Differentiation

    How do you find f'(x), f''(x) of f(x) =ln (1-x) IF f(x) = ln (1-x) Then use the chain rule with u(x) = 1-x f(u) = ln u df/dx = df/du du/dx f'(x) = -1/(1-x) Use the chain rule again: f"(x) = -[-1/(1-x)^2]*(-1) = -1/(1-x)^2 What is

    asked by Jill on November 25, 2006
  5. 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

    asked by Confused on February 21, 2007
  6. Calc

    I'm creating a "calculu for dummies" project book. I've already done most of it, I'm just stuck on these ones. Thank you! -What is the definition of a derivative? -What does the derivative of a function tell you (in english) ?

    asked by Jill on May 19, 2011
  7. calc

    find the derivative of y = sqrt(9 - 16x) Use the chain rule. First find the derivative of the sqrt, and multiply that by the derivative of what is contained inside. Cake. Use the chain rule. If we have y(x)=sqrt(9-16x) then

    asked by joe on September 27, 2006
  8. Math - Calculus Question.

    hey can someone explain to me the relationship between the chain rule and implicit differentiation? It would be very much appreicated, thanks The chain rule is utilized whenever you have a function within a function such as cos^2

    asked by Andrew D on December 6, 2006
  9. calculus

    Please help, my live tutor and I could spent 2 hours trying to solve these two: find an equation for tangent line y=-1-8^2@ (-4,-129) find the derivative of the function:----we both kept getting the same answer, but Mathlab kept

    asked by Pam on April 25, 2008
  10. Calculus

    Find the derivative of [(2+x)/(x-3)]^(2/5) I tried the power of a function rule, quotient rule, the chain rule but keep getting stuck.

    asked by Sam on January 28, 2018

More Similar Questions