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Math Help - chain rule question

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    chain rule question

    f(x) = sin(csc x -tan^2 (2x))

    f'(x) = cos(csc x -tan^2 (2x))[ -csc x cot x -2 tan(2x)(sec^2(2x))(2)]


    Why in the secont line is it 2tan(2x) instead of sec^2(2x)? cos is the derivative of sine and -csc(x)cot(x) is the derivative of csc x. Is it that the derivative of tan^2(x) is just like taking the derivative of x^2 but where x=tan(x)?
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    Re: chain rule question

    Quote Originally Posted by kingsolomonsgrave View Post
    f(x) = sin(csc x -tan^2 (2x))

    f'(x) = cos(csc x -tan^2 (2x))[ -csc x cot x -2 tan(2x)(sec^2(2x))(2)]


    Why in the secont line is it 2tan(2x) instead of sec^2(2x)? cos is the derivative of sine and -csc(x)cot(x) is the derivative of csc x. Is it that the derivative of tan^2(x) is just like taking the derivative of x^2 but where x=tan(x)?
    That's it exactly. Beast of a derivative, isn't it?

    -Dan
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    Re: chain rule question

    sure is!
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