If z = frac{y}{x} left[ sin left( frac{x}{y} | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The given function is $z = f\left( \frac{x}{y} \right)$. This implies that $z$ is a homogeneous function of $x$ and $y$ with degree $n = 0$. Accor

Vedclass · Accepted Answer

$-y \frac{\partial z}{\partial y}$

Vedclass · Answer

(B) The given function is $z = f\left( \frac{x}{y} \right)$. This implies that $z$ is a homogeneous function of $x$ and $y$ with degree $n = 0$. According to Euler's theorem for homogeneous functions,if $z$ is a homogeneous function of degree $n$,then $x \frac{\partial z}{\partial x} + y \frac{\partial z}{\partial y} = nz$. Since $n = 0$,we have $x \frac{\partial z}{\partial x} + y \frac{\partial z}{\partial y} = 0 \cdot z = 0$. Therefore,$x \frac{\partial z}{\partial x} = -y \frac{\partial z}{\partial y}$.

If $z = \frac{y}{x} \left[ \sin \left( \frac{x}{y} \right) + \cos \left( 1 + \frac{y}{x} \right) \right]$,then $x \frac{\partial z}{\partial x} = $

Similar Questions

If $u=\log \left(x^3+y^3+z^3-3 x y z\right)$,then $(x+y+z)(u_x+u_y+u_z)$ is equal to

If $u = \tan^{-1}\left(\frac{x^3 + y^3}{x - y}\right)$,then $x\frac{\partial u}{\partial x} + y\frac{\partial u}{\partial y} = $

If $f(x, y) = \frac{\cos(x - 4y)}{\cos(x + 4y)}$,then $\left. \frac{\partial f}{\partial x} \right|_{y = \frac{x}{4}}$ is equal to:

If $u=\sin ^{-1}\left(\frac{x^4+y^4}{x+y}\right)$,then $x \frac{\partial u}{\partial x}+y \frac{\partial u}{\partial y}$ is equal to

If ${z^2} = \frac{{x^{1/2} + y^{1/2}}}{{x^{1/3} + y^{1/3}}}$,then $x\frac{{\partial z}}{{\partial x}} + y\frac{{\partial z}}{{\partial y}} = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module