# Partial Derivative – A function with log – Exercise 3286

Exercise

Find the partial derivatives of the function

$$z(x,y)={(1+\log_y x)}^3$$

$$z'_x (x,y)=\frac{3}{x\ln y}{(1+\frac{\ln x}{\ln y})}^2$$
$$z'_y (x,y)=3{(1+\frac{\ln x}{\ln y})}^2\cdot \frac{-\ln x}{y\ln^2 y}$$