Partial Derivative – A function to the power of a function – Exercise 3250

Exercise

Find the partial derivatives of the function

$$z(x,y)={(1+xy)}^y$$

$$z'_x (x,y)=y^2{(1+xy)}^{y-1}$$
$$z'_y (x,y)={(1+xy)}^y(\ln (1+xy)+\frac{xy}{1+xy})$$