Results 1 to 2 of 2

Math Help - [SOLVED] Is this double derivative correct?

  1. #1
    Newbie
    Joined
    Oct 2008
    Posts
    16

    [SOLVED] Is this double derivative correct?

    Given:

    <br />
f(x) = \frac{x^2}{x^2 + 4}<br />


    Using the quotient rule, I found that:

    <br />
f'(x) = \frac{8x}{(x^2 + 4)^2}<br />

    <br />
f''(x) = \frac{-8(3x^4 + 8x^2 - 16)}{(x^2 + 4)^4}<br />


    Is this correct? I am a little suspicious of f''(x). It seems to be a little too big, but I can't seem to find any mistake in my work.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member
    Joined
    Sep 2008
    Posts
    31
    Your 1st derivative is definitely correct. Now I'll check the second derivative:

    <br />
f''(x) = \frac{8(x^2+4)^2 - (8x)(4x)(x^2+4)}{(x^2+4)^4}<br />

    Simplifying:
    <br />
f''(x) = \frac{8*(x^2+4)^2 - 32x^2 * (x^2+4)}{(x^2+4)^4} = <br />
\frac{8x^4 + 64x^2 + 128 - 32x^4 - 128x^2}{(x^2+4)^4}<br />

    More simplifying:
    <br />
f''(x) = \frac{-8(3x^4 + 8x^2 - 16}{(x^2 + 4)^4}<br />
    So you are correct.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Simple ODE need to double check if correct
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: September 19th 2011, 03:34 AM
  2. [SOLVED] Correct double angle working?
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: April 9th 2010, 02:15 AM
  3. Replies: 1
    Last Post: December 12th 2009, 09:52 PM
  4. Does this derivative look correct?
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 10th 2009, 09:51 PM
  5. is this derivative correct?
    Posted in the Calculus Forum
    Replies: 4
    Last Post: March 4th 2008, 09:49 AM

Search Tags


/mathhelpforum @mathhelpforum