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Math Help - chain rule function!

  1. #1
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    chain rule function!

    am trying to sort out this problem below;

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

    this time the function is raise to a quadratic equation.

    thanks
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  2. #2
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    Re: chain rule function!

    Quote Originally Posted by lawochekel View Post
    am trying to sort out this problem below;

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

    this time the function is raise to a quadratic equation.

    thanks
    Logarithmic differentiation will probably be your best bet here.

    Let y = (1-x^2)^{a+bx+cx^2} so that \ln(y) = (a+bx+cx^2)\ln(1-x^2)

    Expanding the brackets gives: \ln(y) = a\ln(1-x^2) + bx\ln(1-x^2) + cx^2\ln(1-x^2)

    Now you can use the chain rule (and don't forget the differentiate the LHS too) and the product rules
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