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Math Help - Derivative Problem

  1. #1
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    Derivative Problem

    Would someone tell me how would you solve the following:
    1) Find \frac{\partial z}{\partial y}
    z=sin(x^3 e^{y}-4y^5)

    this is what i have done, but i don't think its correct.

    \frac{\partial z}{\partial y}=x^3 e^y-20y^4cos(x^3 e^{y}-4y^5)

    P.S
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  2. #2
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    z = \sin{(x^3e^y - 4y^5)}.

    Let u = x^3e^y - 4y^5 so that z = \sin{u}.


    \frac{\partial u}{\partial y} = x^3e^y - 20y^4.


    \frac{dz}{du} = \cos{u} = \cos{(x^3e^y - 4y^5)}.


    Therefore \frac{\partial z}{\partial y} = (x^3e^y - 20y^4)\cos{(x^3e^y - 4y^5)}.


    I agree with your answer, as long as you put the brackets where they're needed.
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