Differentiation Question 91
Question: If $ u=xy^{2}{{\tan }^{-1}}( \frac{y}{x} ) $ , then $ xu _{x}+yu _{y}= $
[EAMCET 2001]
Options:
A) 2u
B) u
C) 3u
D) u/3
Show Answer
Answer:
Correct Answer: C
Solution:
$ u=x^{3}{{( \frac{y}{x} )}^{2}}{{\tan }^{-1}}( \frac{y}{x} ) $ is homogeneous in x, y of degree 3.
$ \therefore $ $ xu _{x}+yu _{y}=3u $ .
BETA
