Results 1 to 5 of 5

Math Help - simple differentiation

  1. #1
    Senior Member furor celtica's Avatar
    Joined
    May 2009
    Posts
    271

    simple differentiation

    I'm supposed to differentiate [(sqrt(x))+1]^2/x
    I thought this would be fairly straightforward even though I haven't learnt how to differentiate multiplications and divisions of functions.
    So I developed [(sqrt(x))+1]^2 to end up with x+2(sqrt(x))+1, which gives me the three terms x/x + 2(sqrt(x))/x + 1/x, which differentiating separately gives me the final result:
    -1/x(sqrt(x)) - 1/(x^2)
    But this is incorrect apparently, where did I go wrong?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member sbhatnagar's Avatar
    Joined
    Sep 2011
    From
    New Delhi, India
    Posts
    200
    Thanks
    17

    Re: simple differentiation

    You did not go wrong anywhere. The correct answer is -\frac{1}{x^2}-\frac{1}{x\sqrt{x}}

    For further information you can refer to this link:

    d/dx (1+sqrt(x))^2/x - Wolfram|Alpha
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4

    Re: simple differentiation

    Quote Originally Posted by furor celtica View Post
    I'm supposed to differentiate [(sqrt(x))+1]^2/x
    I thought this would be fairly straightforward even though I haven't learnt how to differentiate multiplications and divisions of functions.
    So I developed [(sqrt(x))+1]^2 to end up with x+2(sqrt(x))+1, which gives me the three terms x/x + 2(sqrt(x))/x + 1/x, which differentiating separately gives me the final result:
    -1/x(sqrt(x)) - 1/(x^2)
    But this is incorrect apparently, where did I go wrong?
    Try rearranging it into the format expected:

    -\frac{1}{x\sqrt{x}}-\frac{1}{x^2}=-\frac{1}{x^{3/2}}-\frac{1}{x^2}=-\frac{1}{x^2}(\sqrt{x}+1)

    CB
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member furor celtica's Avatar
    Joined
    May 2009
    Posts
    271

    Re: simple differentiation

    the answer given is
    1 - 1/(x(sqrt(x))) - 2/(x^3)
    Is this just another form for the same result, or a legit mistake in the textbook?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member ILikeSerena's Avatar
    Joined
    Dec 2011
    Posts
    733
    Thanks
    121

    Re: simple differentiation

    Quote Originally Posted by furor celtica View Post
    the answer given is
    1 - 1/(x(sqrt(x))) - 2/(x^3)
    Is this just another form for the same result, or a legit mistake in the textbook?
    That would be a mistake in the textbook.
    That expression is not the derivative of [(sqrt(x))+1]^2/x.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Simple Differentiation 2 :)
    Posted in the Calculus Forum
    Replies: 3
    Last Post: November 29th 2009, 02:35 PM
  2. Replies: 2
    Last Post: November 12th 2009, 04:09 PM
  3. Simple Differentiation
    Posted in the Calculus Forum
    Replies: 4
    Last Post: August 28th 2009, 04:16 AM
  4. A simple differentiation
    Posted in the Calculus Forum
    Replies: 2
    Last Post: April 30th 2009, 07:59 AM
  5. Simple log differentiation
    Posted in the Calculus Forum
    Replies: 2
    Last Post: January 7th 2008, 03:40 PM

Search Tags


/mathhelpforum @mathhelpforum