Results 1 to 4 of 4

Math Help - exponential function derivative

  1. #1
    Newbie
    Joined
    May 2009
    Posts
    3

    exponential function derivative

    Can anyone help me find the derivative of y=2^|x|?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    -1
    e^(i*pi)'s Avatar
    Joined
    Feb 2009
    From
    West Midlands, England
    Posts
    3,053
    Thanks
    1
    Quote Originally Posted by nejikun View Post
    Can anyone help me find the derivative of y=2^|x|?
    If f(x) = a^x then f'(x) = a^xln(a)

    Spoiler:
    Take the log of both sides:

    ln(y) = ln(2^{|x|}) = |x|ln(2)

    Differentiate both sides:

    \frac{1}{y} \cdot \frac{dy}{dx} = ln(2)

    Isolate dy/dx:

    \frac{dy}{dx} = yln(2) = 2^{|x|}ln(2)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member TheAbstractionist's Avatar
    Joined
    Apr 2009
    Posts
    328
    Thanks
    1
    Quote Originally Posted by nejikun View Post
    Can anyone help me find the derivative of y=2^|x|?
    Hi nejikun.

    y\ =\ 2^{|x|}\ =\ e^{(\ln2)|x|}\ =\ e^u where u=(\ln2)|x|

    So, using the chain rule, \frac{dy}{dx}\ =\ \frac{dy}{du}\,\frac{du}{dx}\ =\ e^u\cdot(\ln2)\frac{|x|}x\ =\ \frac{(\ln2)|x|}x2^{|x|}.

    Note that \frac{d\left(|x|\right)}{dx}=\frac{|x|}x.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member TheAbstractionist's Avatar
    Joined
    Apr 2009
    Posts
    328
    Thanks
    1
    Quote Originally Posted by e^(i*pi) View Post
    ln(y) = ln(2^{|x|}) = |x|ln(2)

    Differentiate both sides:

    \frac{1}{y} \cdot \frac{dy}{dx} = ln(2)
    The derivative of |x| is 1 if x>0 and -1 if x<0; i.e. \frac{d(|x|)}{dx}=\frac{|x|}x.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. derivative of exponential function
    Posted in the Calculus Forum
    Replies: 3
    Last Post: March 23rd 2010, 11:30 AM
  2. Derivative of exponential function
    Posted in the Calculus Forum
    Replies: 1
    Last Post: January 27th 2010, 06:00 AM
  3. derivative of exponential function
    Posted in the Calculus Forum
    Replies: 2
    Last Post: February 20th 2009, 12:43 AM
  4. First derivative of exponential function
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 31st 2008, 02:24 PM
  5. Derivative of Exponential Function
    Posted in the Calculus Forum
    Replies: 5
    Last Post: April 10th 2008, 06:23 PM

Search Tags


/mathhelpforum @mathhelpforum