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Thread: Derivative

  1. #1
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    Derivative

    How do I find the derivative of ​$y=sin(tan\,x^2)$

    Any help will be appreciated.
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  2. #2
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    Re: Derivative

    just use the chain rule

    $\dfrac{dy}{dx} = \cos(\tan(x^2)) \cdot \sec^2(x^2)\cdot 2x = 2x \sec^2(x^2) \cos(\tan(x^2))$
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  3. #3
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    Re: Derivative

    Use chain rule,i.e.,

    $\dfrac{d}{dx}f(g(x))=f'(g(x))g'(x)$

    $\Rightarrow \cos(\tan\,x^2) .\dfrac{d}{dx} (\tan\,x^2)$

    $\Rightarrow \cos(\tan\,x^2) \sec^2 (x^2) 2\,x$

    Here is the similar question with complete solution

    http://www.actucation.com/calculus-1...tric-functions
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  4. #4
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    Re: Derivative

    Quote Originally Posted by Natar View Post
    How do I find the derivative of ​$y=sin(tan\,x^2)$

    Any help will be appreciated.
    $f(x)=\sin(x)$

    $g(x)=\tan(x)$

    $h(x)=x^2$

    $\dfrac{d}{dx}\bigg[f[g(h(x))]\bigg] = \color{red}{f'[g(h(x))]} \cdot \color{blue}{g'(h(x))} \cdot \color{green}{h'(x)}$

    $\color{red}{\cos[\tan(x^2)]} \cdot \color{blue}{\sec^2(x^2)} \cdot \color{green}{2x}$
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  5. #5
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    Re: Derivative

    Quote Originally Posted by deesuwalka View Post

    $\Rightarrow \cos(\tan\,x^2) \sec^2 (x^2) 2\,x$
    You would not use a "times" sign for multiplication, and especially not separating that quantity for the final form.

    At a minimum, you would use a style in post #4 using the multiplication dots, although it is common to place the
    "2x" to the far left if someone were to keep simplifying with any additional step(s).
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