# If $u=f\large\left(\frac {y}{x} \right)$ then $x\large\frac{\partial u}{\partial x}$+$y\large\frac{\partial u}{\partial y}$ is equal to

$\begin{array}{1 1}(1)0&(2)1\\(3)2u&(4)u\end{array}$

$u=f( \large\frac{y}{x})$
u is a homogeneous function of degree 0
Euler's theorem,
$x \large\frac{\partial u}{\partial x} $$+ y \large\frac{\partial u}{\partial y}$$=0.f$
$x \large\frac{\partial u}{\partial x} $$+ y \large\frac{\partial u}{\partial y}$$=0$
Hence 1 is the correct answer.
answered May 20, 2014 by