# Derivative of Implicit Multivariable Function – Calculating partial derivatives to two-variable function – Exercise 4342

Exercise

The equation (with parameter a)

$$x^2+y^2+z^2=a^2$$

Defines the implicit function

$$z(x,y)$$

Find its partial derivative z‘_x, z’_y.

$$z'_x(x,y)=\frac{-x}{z}$$
$$z'_y(x,y)=\frac{-y}{z}$$