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- Euler's Theorem: If $f(x,y)$ is a homogeneous function of degree n, then $x\large\frac{\partial f}{\partial x}$$+y\large\frac{\partial f}{\partial y}$$=nf$ This can be extended to several variables

$u=\sqrt {x^2+y^2}$

Step 1:

u is a homogeneous function in x,y of degree 1.

$\therefore $ by Euler's Theorem ,

$x\large\frac{\partial u}{\partial x}$$+y\large\frac{\partial u}{\partial y}$$=1u$

Step 2:

$x\large\frac{\partial u}{\partial x}$$+y \large \frac{\partial u}{\partial y}$$=u$

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