Differentiation Question 84
Question: If $ z={{\sin }^{-1}}( \frac{x+y}{\sqrt{x}+\sqrt{y}} ) $ , then $ x\frac{\partial z}{\partial x}+y\frac{\partial z}{\partial y} $ is equal to
[EAMCET 1998; Orissa JEE 2000]
Options:
A) $ \frac{1}{2}\sin z $
B) $ \frac{1}{2}\tan z $
C) $ 0 $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
$ \sin z $ is homogeneous in x, y of degree 1/2.
$ \therefore $ $ x\frac{\partial }{\partial x}(\sin z)+y\frac{\partial }{\partial y}(\sin z)=\frac{1}{2}\sin z $
Therefore $ \frac{dv}{dt} $
Therefore $ x\frac{\partial z}{\partial x}+y\frac{\partial z}{\partial y}=\frac{1}{2}\tan z $ .
BETA
