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## Homework Statement

Given:

[tex]\varphi(t)[/tex] – differentiable function.

[tex]z=z(x,y)[/tex] – differentiable function.

And there is the following equation:

[tex]x^2 + y^2 + z^2 = \varphi (ax+by+cz)[/tex]

where [tex]a,b,c[/tex] are constants,

Prove that:

[tex](cy - bz)\cdot \frac {\partial z}{\partial x} + (az-cx)\cdot \frac{\partial z}{\partial y} = bx - ay [/tex]

## The Attempt at a Solution

I tried to take partial derivatives of both sides with respect to x and then with respect to y. But I don't know how to differentiate the right-hand side of the equation.

Also if I did, what should I had done next?