If $(x + y)\sin{u = x^{2}y^{2},\ }\ then\ x\frac{\partial u}{\partial x} + y\frac{\partial u}{\partial y}$ is equal to

Question

Dr. Abubacker · Accepted Answer

(d)
$f(x,y) = \sin u = \frac{x^{2}y^{2}}{x + y}\$
Here, $f(x)$ is a homogenous function of degree 3. By Euler theorem,
$x\ \frac{\partial f}{\partial x} + y\frac{\partial f}{\partial y} = 3f$
$x\ \frac{\partial\sin u}{\partial x} + y\ \frac{\partial\sin u}{\partial y} = 3\sin u$
$\Rightarrow \ x\frac{\partial u}{\partial x} + y\frac{\partial u}{\partial y} = 3	an u\ \ \ \ \ \ \ \ \ \ \$

Q. If $(x + y)\sin{u = x^{2}y^{2},\ }\ then\ x\frac{\partial u}{\partial x} + y\frac{\partial u}{\partial y}$ is equal to

Explanation

Reviewed by Dr. Abubacker

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