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Math Help - derivative of f(x)=tan^2x^2

  1. #1
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    derivative of f(x)=tan^2x^2

    Can someone please show me the steps to this problem? Thanks alot
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  2. #2
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    Re: derivative of f(x)=tan^2x^2

    Use the chain rule twice here.

    Say y = \tan ^2x^2

    Find \frac{dy}{dx} where u = \tan x^2 \implies y = u^2

    what do you get?
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  3. #3
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    Re: derivative of f(x)=tan^2x^2

    Quote Originally Posted by jmanna98 View Post
    Can someone please show me the steps to this problem? Thanks alot
    The derivative of f^2(x^2) is 2[f(x^2)]f'(x^2)(2x).
    Last edited by Plato; August 11th 2011 at 02:16 AM.
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  4. #4
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    Re: derivative of f(x)=tan^2x^2

    f(x)=tan^2x^2
    f'(x)=(tanx^2)^2
    f'(x)=2(tanx^2)[sec(x^2)(2x)]

    Where am I making errors? I am unsure if I am understanding the chain rule properly for trig functions.

    My understanding is that you take the derivative of the outside function multiplied by the inside function and multiplied by the derivative of the inside function.
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  5. #5
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    Re: derivative of f(x)=tan^2x^2

    Quote Originally Posted by jmanna98 View Post
    f'(x)=2(tanx^2)[sec(x^2)(2x)]
    That looks correct to me.
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  6. #6
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    Re: derivative of f(x)=tan^2x^2

    You're close. \frac{d}{dx}\tan(x) = \sec^{2}(x) \ne \sec(x)
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  7. #7
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    Re: derivative of f(x)=tan^2x^2

    oh...thats what I meant. My bad. Thanks for the confirmation!
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