# Partial Derivative – A three variable function – Exercise 3279

Exercise

Find the partial derivatives of the function

$$u(x,y,z)=x^{\frac{y}{z}}$$

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