# Derivative of Implicit Multivariable Function – Calculate partial derivatives to an equation with an exponential – Exercise 6481

Exercise

Given that the equation

$$e^{x+y+z}=(x^2+y^2)\cdot z+1$$

Defines the implicit function

$$x(y,z)$$

Calculate its partial derivatives at the origin

$$x'_y(0,0),x'_z(0,0)$$

$$x'_y(0,0)=-1$$
$$x'_z(0,0)=-1$$