# Partial Derivative – A ln function inside a ln function – Exercise 3273

Exercise

Find the partial derivatives of the function

$$z(x,y)=\ln (x+\ln y)$$

$$z'_x (x,y)=\frac{1}{x+\ln y}$$
$$z'_y (x,y)=\frac{1}{x+\ln y}\cdot \frac{1}{y}$$