Differentiation Question 80
Question: If $ u={{\tan }^{-1}}\frac{y}{x} $ , then by Euler’s Theorem the value of x $ \frac{\partial u}{\partial x}+y\frac{\partial u}{\partial y}= $
[Tamilnadu (Engg.) 1993]
Options:
A) $ \tan u $
B) $ \sin u $
C) $ 0 $
D) $ \cos 2u $
Show Answer
Answer:
Correct Answer: C
Solution:
$ u={{\tan }^{-1}}\frac{y}{x}=x^{0}.{{\tan }^{-1}}\frac{y}{x} $
Clearly u is homogeneous in x, y of degree 0.
$ \therefore $ By Euler’s theorem $ x\frac{\partial u}{\partial x}+y\frac{\partial u}{\partial z}=0.u=0 $ .
BETA
