Differentiation Question 99
Question: If $ z=\frac{y}{x}[ \sin \frac{x}{y}+\cos ( 1+\frac{y}{x} ) ] $ , then $ x\frac{\partial z}{\partial x}= $
[EAMCET 2002]
Options:
A) $ y\frac{\partial z}{\partial y} $
B) $ -y\frac{\partial z}{\partial y} $
C) $ 2y\frac{\partial z}{\partial y} $
D) $ 2y\frac{\partial z}{\partial x} $
Show Answer
Answer:
Correct Answer: B
Solution:
Since z is homogeneous in x, y of order -0…….
$ \therefore $ By Euler’s theorem $ x\frac{\partial z}{\partial x}+y\frac{\partial z}{\partial y}= $ 0
Therefore $ x\frac{\partial z}{\partial x}=-y\frac{\partial z}{\partial y} $
BETA
