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Math Help - composite / chain rule....differentiate

  1. #1
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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. #2
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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. #3
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    its the second option ....
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  4. #4
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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. #5
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    so can i just check that the anwser will be

    -sin(x)+cos(x)

    thanx
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  6. #6
    Super Member craig's Avatar
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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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