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Math Help - derivative 3

  1. #1
    Senior Member euclid2's Avatar
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    derivative 3

    determine the derivative of y=3e^{sin(x+2)}
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  2. #2
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    Quote Originally Posted by euclid2 View Post
    determine the derivative of y=3e^{sin(x+2)}
    u=x+2

    v=sinu

    w=e^v

    y=3w


    \displaystyle\frac{dy}{dx}=\frac{dy}{dw}\, \frac{dw}{dv}\, \frac{dv}{du}\, \frac{du}{dx}
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  3. #3
    Senior Member euclid2's Avatar
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    is this the chain rule? i'm not familiar with the chain rule is there another way to do it?
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  4. #4
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    Quote Originally Posted by euclid2 View Post
    is this the chain rule? i'm not familiar with the chain rule is there another way to do it?
    Yes that is the chain rule and it's the only way to solve this question.

    Archie Meade's way is best

    If you let u = \sin(x+2) then you can find \frac{du}{dx} without much difficulty (although you're using the chain rule the derivative of x is 1 so it makes no numerical difference in this case)

    Thus you have y = 3e^u which you should know how to solve.

    I must stress that this is still the chain rule though
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  5. #5
    Senior Member euclid2's Avatar
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    ok so:



    f '(x) = 3 * cos(x + 2) * e ^ ((sin(x + 2))

    correct ?
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  6. #6
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    Except for the wrong number of left parentheses on ((sin(x+ 2)), yes, it is correct.

    See, isn't the chain rule nice?
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