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Math Help - differentiate f(x) using chain rule (i think?)

  1. #1
    Junior Member
    Joined
    Oct 2008
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    differentiate f(x) using chain rule (i think?)

    Differentiate the function. You do not need to simplify your answer

    f(x)=sin(cos3x)+cos(5sinx)

    i thought in order to go about doing this you had to usethe chain rule for
    each component


    d/dx(sin(cos3x))+d/dx(cos(5sinx))

    d/dx(sin(cos3x))
    using chain rule = cos(cos3x)* -sin3x


    d/dx(cos(5sinx))
    using chain rule = -sin(5sinx)* 5cosx


    so f '(x) = [cos(cos3x)* -sin3x] + [-sin(5sinx)* 5cosx]

    all this is a new concept just recently learned in my math class, and i really don't know what i'm doing. hopefully i'm somewhat on the right track??
    thanks in advance!
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  2. #2
    MHF Contributor
    Joined
    Mar 2007
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    1,240

    Talking

    Don't forget to go all the way down to "x". When you differentiate "cos(3x)", you differentiate the cosine, and then the 3x!

    . . . . . \frac{d(\sin{(\cos{(3x)}})}{dx}\, =\, \cos{(\cos{(3x)})}\,\times\, \-\sin{(3x)}\,\times\,3

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