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Math Help - function of a function differentiation!

  1. #1
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    function of a function differentiation!

    Hi, pls trying to solve the differentiation problem below, what best method can one use to solve it.

    (1+x^2)^a + bx + cx^2

    thanks.

    Moderator edit: [tex] tags not [tex] tags are required when using latex.
    Last edited by mr fantastic; December 12th 2011 at 03:09 AM. Reason: Fixed latex - replaced [math] tags with [tex] tags.
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  2. #2
    MHF Contributor Amer's Avatar
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    Re: function of a function differentiation!

    Quote Originally Posted by lawochekel View Post
    Hi, pls trying to solve the differentiation problem below, what best method can one use to solve it.

    (1+x^2)^a+bx+cx^2

    thanks.
    (1+x^2)^a + bx + cx^2

    you need to know the chain rule
    what do you know about differentiation ??
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  3. #3
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    Re: function of a function differentiation!

    Quote Originally Posted by lawochekel View Post
    Hi, pls trying to solve the differentiation problem below, what best method can one use to solve it.

    (1-x^2)^a+bx+cx^2

    thanks.
    I am assuming a,b and c are constants.

    To make this easier you can differentiate each of the terms separately: \dfrac{d}{dx}((1-x^2)^a+bx+cx^2) = \dfrac{d}{dx}(1-x^2)^a + \dfrac{d}{dx} bx +  \dfrac{d}{dx} cx^2

    For the second and third terms you can use the power rule \left(\dfrac{d}{dx} ax^n = anx^{n-1}\right).

    For the first term you need to use the chain rule.
    Let u = 1-x^2 then \dfrac{d}{dx}(1-x^2)^a = \dfrac{d}{du} \cdot \dfrac{du}{dx}

    In your case \dfrac{d}{dx}(1-x^2)^a = \dfrac{d}{du} u^a \cdot \dfrac{du}{dx}.

    I'll leave you to figure the rest out, if you get stuck please post what you've tried
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