Results 1 to 2 of 2

Math Help - Find 1st and 2nd Derivative.

  1. #1
    Affinity
    Guest

    Find 1st and 2nd Derivative.

    Find the first derivative and then the second derivative of
    Thank you in advance!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    10
    Quote Originally Posted by Affinity View Post
    Find the first derivative and then the second derivative of
    Thank you in advance!
    y=\frac{e^x}{x^2}

    y'=\frac{(e^x)'(x^2)-(e^x)(x^2)'}{(x^2)^2}
    y'=\frac{x^2e^x-2xe^x}{x^4}=\frac{xe^x(x-2)}{x^4}=\frac{e^x(x-2)}{x^3}

    y''=\frac{[e^x(x-2)]'(x^3)-[e^x(x-2)](x^3)'}{(x^3)^2}
    y''=\frac{[(e^x)'(x-2)+e^x(x-2)']x^3-e^x(x-2)(x^3)'}{x^6}
    y''=\frac{[e^x(x-2)+e^x]x^3-3x^2e^x(x-2)}{x^6}
    y''=\frac{e^x(x-2)x^3+x^3e^x-3x^2e^x(x-2)}{x^6}=\frac{e^x[(x-2)x^3+x^3-3x^2(x-2)]}{x^6}
    y''=\frac{e^x(x^4-2x^3+x^3-3x^3+6x^2)}{x^6}=\frac{e^x(x^4-4x^3+6x^2)}{x^6}= \frac{x^2e^x(x^2-4x+6)}{x^6}
    y''=\frac{e^x(x^2-4x+6)}{x^4}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Find derivative.
    Posted in the Algebra Forum
    Replies: 1
    Last Post: October 11th 2010, 08:46 AM
  2. Find the derivative of: (1-x)*ln(1-x)
    Posted in the Calculus Forum
    Replies: 2
    Last Post: December 29th 2009, 09:35 AM
  3. find derivative
    Posted in the Calculus Forum
    Replies: 8
    Last Post: August 10th 2009, 11:36 AM
  4. find the second derivative of...
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 16th 2009, 08:06 PM
  5. find the Derivative
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 26th 2008, 06:35 PM

/mathhelpforum @mathhelpforum