Would someone tell me how would you solve the following:

1) Find $\displaystyle \frac{\partial z}{\partial y}$

$\displaystyle z=sin(x^3 e^{y}-4y^5)$

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

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

P.S