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Math Help - Calculus chain rule questions

  1. #1
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    Calculus chain rule questions

    Hi I have a few calculus questions, could you please explain how to get the final answer too, thanks.

    Derivative of :






    dy/dx here

    dy/dx here

    dy/dt here








    Last edited by KK88; May 10th 2010 at 08:37 PM.
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  2. #2
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    Quote Originally Posted by KK88 View Post
    Hi I have a few calculus questions, could you please explain how to get the final answer too, thanks.

    Derivative of :

    Chain rule of the chain rule with a product rule


    chain rule

    dy/dx here
    chain rule
    dy/dx here
    product rule with chain
    dy/dt here
    chain


    You haven't attempted much so start by trying that.
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  3. #3
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    Ok I figured out the middle three but I cannot quite get the first one and last one
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  4. #4
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    (cos\big(e^{x^2cos(x)}\big))^{\frac{1}{2}}

    \frac{1}{2}(cos\big(e^{x^2cos(x)}\big))^{\frac{-1}{2}}(-sin\big(e^{x^2cos(x)}\big))(e^{x^2cos(x)}(2xcos(x)-x^2sin(x)))

    I am not going to simplify that.
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  5. #5
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    e^{2sin(8t)}

    8e^{2sin(8t)}2cos(8t)=16e^{2sin(8t)}cos(8t)
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  6. #6
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    Thanks for the responses.
    The second one is correct however I still cant get the first one right, I input this:

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  7. #7
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    The first one is correct too. Here is the maple output.
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  8. #8
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    \frac{1}{2}(cos\big(e^{x^2cos(x)}\big))^{\frac{-1}{2}}(-sin\big(e^{x^2cos(x)}\big))(e^{x^2cos(x)}(2xcos(x)-x^2sin(x)))

    You need to have this quantity in parenthesis.
    (2xcos(x)-x^2sin(x))
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  9. #9
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    Thanks that did it.
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