# Partial Derivative – A sum of ln function and an exponential function – Exercise 3247

Exercise

Find the partial derivatives of the function

$$z(x,y)=\ln (x+y^2)+5^{xy^2}$$

$$z'_x (x,y)=\frac{1}{x+y^2}+y^2 \ln 5\cdot5^{xy^2}$$
$$z'_y (x,y)=\frac{2y}{x+y^2}+2xy\ln 5\cdot5^{xy^2}$$