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Thread: help with composite rule question

  1. #1
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    help with composite rule question

    Hey can anyone help me with the following question....



    use the composite rule to differentiate f(x) = e^cosx+sinx


    thank you
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  2. #2
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    composite rule is another name for chain rule isn't it?

    differentiate the seperate terms

    so $\displaystyle e^{cos(x)}$ diff's to $\displaystyle -sin(x)(e^{cos(x)})$ using the chain rule (or composite rule (i.e. you diff the first term, then multiply by the diff of term inside brackets)) and $\displaystyle sin(x)$ diff's to $\displaystyle cos(x)$ using standard rules. then just add them together at the end

    $\displaystyle f'(x)=-sin(e^{cos(x)})+cos(x)$ and to be more artistic you would swap them so you don't start with a negative sign.
    Last edited by Rapid_W; Jun 3rd 2009 at 07:08 AM.
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  3. #3
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    if you mean

    $\displaystyle f(x)=e^{cosx+sinx}$

    $\displaystyle f'(x)=\left(\frac{d}{dx}(cosx+sinx)\right)e^{cosx+ sinx}$

    $\displaystyle f'(x)=(-sinx+cosx)e^{cosx+sinx}$
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  4. #4
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    Yup, take your pick depending on what your question is
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  5. #5
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    well using the product rule of

    k'(x)= f'(x)g(x) + f(x) g'(x)

    and the previous equation, can i show the derivitave of the function

    g(x) = (cosx + sinx - 1) e^cosx+sinx

    is g'(x) = (cos^2x - sin^2x)e^cosx +sinx
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  6. #6
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    Quote Originally Posted by Rapid_W View Post
    composite rule is another name for chain rule isn't it?

    differentiate the seperate terms

    so $\displaystyle e^{cos(x)}$ diff's to $\displaystyle -sin(e^{cos(x)})$
    The derivative of $\displaystyle e^{cos(x)}$ is -sin(x) times $\displaystyle e^{cos(x)}$, not -sin of $\displaystyle e^{cos(x)}$ as you write.

    using the chain rule (or composite rule (i.e. you diff the first term, then multiply by the diff of term inside brackets)) and $\displaystyle sin(x)$ diff's to $\displaystyle cos(x)$ using standard rules. then just add them together at the end

    $\displaystyle f'(x)=-sin(e^{cos(x)})+cos(x)$ and to be more artistic you would swap them so you don't start with a negative sign.
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  7. #7
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    oops, missed the x out, simple error, have fixed my original post, thanks for pointing that out.
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