Results 1 to 4 of 4

Math Help - Differentiating funtion of a function

  1. #1
    Newbie
    Joined
    Mar 2011
    Posts
    14

    Differentiating funtion of a function

    I'm differentiating \frac{\sqrt{1-x^2}}{1-x} and coming up with the answer \frac{1-x}{(1-x^2)(1-x)^\frac{1}{2}} and an online differentiator I've run it through gives the same answer. However, the book I'm working from gives the answer as \frac{1}{(1-x)(1-x^2)^\frac{1}{2}}.

    Which of these is correct? Or are they both the same and I'm just missing a way of simplifying my answer?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Master Of Puppets
    pickslides's Avatar
    Joined
    Sep 2008
    From
    Melbourne
    Posts
    5,236
    Thanks
    29
    Maybe they are the same function? You need to use the quotient rule here.

    Show us your working.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Mar 2011
    Posts
    14
    My working goes like this:

    Let u=\sqrt{1-x^2} and v=1-x

    Therefore \frac{du}{dx}=\frac{1}{2}(1-x^2)^\frac{-1}{2}\times -2x=\frac{-x}{(1-x^2)^\frac{1}{2}} and \frac{dv}{dx}=-1

    Therefore

    \frac{dy}{dx}=\frac{(1-x)\frac{-x}{(1-x^2)^\frac{1}{2}}+(1-x^2)^\frac{1}{2}}{(1-x)^2}

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

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

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

  4. #4
    MHF Contributor

    Joined
    Mar 2011
    From
    Tejas
    Posts
    3,401
    Thanks
    762
    you have a common factor of 1-x in the numerator and denominator, so they cancel. your original posted answer is incorrect, your second answer with the work shown IS correct, and equal to the answer in your book.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Differentiating x to a function of x
    Posted in the Calculus Forum
    Replies: 2
    Last Post: September 7th 2010, 04:10 PM
  2. differentiating function
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 5th 2009, 05:45 PM
  3. Inverse function of a funtion
    Posted in the Algebra Forum
    Replies: 6
    Last Post: March 24th 2009, 05:13 AM
  4. Differentiating Bessel funtion
    Posted in the Differential Equations Forum
    Replies: 4
    Last Post: June 18th 2008, 09:18 AM
  5. Replies: 2
    Last Post: March 30th 2008, 11:46 AM

Search Tags


/mathhelpforum @mathhelpforum