Differentiation Question 279
Question: If $ y=\frac{{{\sin }^{-1}}x}{\sqrt{1-x^{2}}} $ , then $ (1-x^{2})\frac{dy}{dx} $ is equal to
[RPET 1995]
Options:
A) $ x+y $
B) $ 1+xy $
C) 1- xy
D) $ xy-2 $
Show Answer
Answer:
Correct Answer: B
Solution:
$ y=\frac{{{\sin }^{-1}}x}{\sqrt{1-x^{2}}} $
$ \frac{dy}{dx}=\frac{\sqrt{1-x^{2}}\frac{1}{\sqrt{1-x^{2}}}-({{\sin }^{-1}}x)\frac{1}{2}\frac{(-2x)}{\sqrt{1-x^{2}}}}{1-x^{2}} $
$ \Rightarrow (1-x^{2})\frac{dy}{dx}=1+x( \frac{{{\sin }^{-1}}x}{\sqrt{1-x^{2}}} )=1+xy $ .
BETA
