# Derivative of Implicit Multivariable Function – Proof of a partial derivative equation – Exercise 6485

Exercise

Given that the function

$$H(u,v)$$

Is differentiable, and that the equation

$$H(\frac{x}{z},\frac{y}{z})=0$$

Defines the implicit function

$$z=f(x,y)$$

Prove the equation

$$x\cdot z'_x+y\cdot z'_y=z$$

Proof

Coming soon…

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