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Thread: composite / chain rule....differentiate

  1. May 28th 2009, 03:47 AM #1
    redieeee_babieeee
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    composite / chain rule....differentiate

    hi can someone lease help with the following question as i have done anythng this hard with the composite/chain rule

    Q) use the composite rule to differentiate the function

    f(x)= e^cos x+ sin x

    thanx
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  2. May 28th 2009, 03:59 AM #2
    pickslides
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    is your equation f(x) = e^{cos(x)}+sin(x) or f(x) = e^{cos(x)+sin(x)} ?

    either way you should employ the rule

    \frac{d}{dx}\left(e^{f(x)}\right) = f'(x)e^{f(x)}<br />
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  3. May 28th 2009, 04:04 AM #3
    redieeee_babieeee
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    its the second option ....
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  4. May 28th 2009, 04:20 AM #4
    craig
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    Quote Originally Posted by redieeee_babieeee View Post
    its the second option ....
    As pickslides said, what you need to do is:

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

    Can you differentiate cos(x)+sin(x)?
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  5. May 29th 2009, 03:47 AM #5
    redieeee_babieeee
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    so can i just check that the anwser will be

    -sin(x)+cos(x)

    thanx
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  6. May 29th 2009, 03:53 AM #6
    craig
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    Quote Originally Posted by redieeee_babieeee View Post
    so can i just check that the anwser will be

    -sin(x)+cos(x)

    thanx
    Yep that's right, I'd write it with the (\cos{x} - \sin{x}) before the e^{cos(x)+sin(x)} for clarities sake, but that's just me being pedantic

    f'(x) = (\cos{x} - \sin{x})e^{cos(x)+sin(x)}
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