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Math Help - Chain Rule Inside of Chain Rule

  1. #1
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    Oct 2009
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    Chain Rule Inside of Chain Rule

    I recently just took a Derivative Mastery Test...and although i passed, there was one problem that just stumped me and i could use some help so i dont make this mistake again.

    Here's the problem:

    Find Derivative of Arcsin(tan(3x^2))
    and thats it...
    Please and Thank you if you can give me a run through
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  2. #2
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    f(x)=\arcsin(\tan(3x^2))

    f'(x) = \frac{1}{\sqrt{1-\tan^2(3x^2)}}\cdot \sec^2(3x^2)\cdot 6x.

    Simplify.
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  3. #3
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    A run through:

    Let's say your f(x) = g(h(q(x)))
    With the chain rule it would be g'(h(q(x))) times h'(q(x)) times q'(x)
    Then it's like what scorpion posted,
    g'(h(q(x))) = \frac{1}{\sqrt{1-\tan^2(3x^2)}}
    remember derivative of arcsin x = \frac{1}{\sqrt{1-x^2}}
    h'(q(x))= \sec^2(3x^2)
    q'(x)=  6x
    Last edited by endling; October 22nd 2009 at 08:43 PM. Reason: Forgot the math tags
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  4. #4
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    Thanks for the answer. I get how that goes about now.
    Thanks Again
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