Results 1 to 4 of 4

Math Help - Function derivative

  1. #1
    Newbie
    Joined
    Feb 2010
    From
    Originally from Indianapolis, Indiana - but currently live in Haarlem, The Netherlands
    Posts
    18

    Function derivative

    I am going through a practice exam and the following question has me perplexed:

    Determine the derivative, with respect to the variable x, of each function below:

    A) f(x) = e^x/(1+e^x)

    B) f(x) = ln(1+x^2)

    I understand the principles of functions, however the "e" is throwing me off in relation. What formulas should I use to solve and what steps to get the correct answers?

    Thank you,

    Matty
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,004
    Thanks
    1660
    Quote Originally Posted by AnAmericanInNederlands25 View Post
    I am going through a practice exam and the following question has me perplexed:

    Determine the derivative, with respect to the variable x, of each function below:

    A) f(x) = e^x/(1+e^x)
    Use the quotient rule and the fact that the derivative of e^x is just e^x

    B) f(x) = ln(1+x^2)
    Use the chain rule and the fact that the derivative of ln(x) is just \frac{1}{x}

    I understand the principles of functions, however the "e" is throwing me off in relation. What formulas should I use to solve and what steps to get the correct answers?

    Thank you,

    Matty
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Feb 2010
    From
    Originally from Indianapolis, Indiana - but currently live in Haarlem, The Netherlands
    Posts
    18
    I guess I am still confused by what that means exactly... Sorry...
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,894
    Thanks
    691
    Quote Originally Posted by AnAmericanInNederlands25 View Post
    I guess I am still confused by what that means exactly... Sorry...
    f(x) = \frac{e^x}{1 + e^x}

    note that the derivative of e^x is e^x , then use the quotient rule ...

    f'(x) = \frac{(1+e^x)e^x - e^x(e^x)}{(1+e^x)^2}

    now clean up the algebra





    f(x) = \ln(1+x^2)

    note that \frac{d}{dx} \ln(u) = \frac{1}{u} \cdot \frac{du}{dx}

    f'(x) = \frac{2x}{1+x^2}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Derivative of function f(x)=x|x|
    Posted in the Calculus Forum
    Replies: 7
    Last Post: August 10th 2010, 11:28 AM
  2. Derivative of function
    Posted in the Calculus Forum
    Replies: 2
    Last Post: August 9th 2010, 12:34 PM
  3. Derivative of Log Function
    Posted in the Calculus Forum
    Replies: 7
    Last Post: October 31st 2009, 08:32 PM
  4. derivative function
    Posted in the Calculus Forum
    Replies: 3
    Last Post: August 1st 2009, 09:48 PM
  5. Derivative of 1-1 function
    Posted in the Calculus Forum
    Replies: 3
    Last Post: July 29th 2009, 06:07 AM

Search Tags


/mathhelpforum @mathhelpforum