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Math Help - 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 e^{cos(x)} diff's to -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 sin(x) diff's to cos(x) using standard rules. then just add them together at the end

    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; June 3rd 2009 at 07:08 AM.
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  3. #3
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    if you mean

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

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

    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 e^{cos(x)} diff's to -sin(e^{cos(x)})
    The derivative of e^{cos(x)} is -sin(x) times e^{cos(x)}, not -sin of 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 sin(x) diff's to cos(x) using standard rules. then just add them together at the end

    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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