Differentiation Question 393
Question: If $ y=\sqrt{(1-x)(1+x)} $ , then
Options:
A) $ (1-x^{2})\frac{dy}{dx}-xy=0 $
B) $ (1-x^{2})\frac{dy}{dx}+xy=0 $
C) $ (1-x^{2})\frac{dy}{dx}-2xy=0 $
D) $ (1-x^{2})\frac{dy}{dx}+2xy=0 $
Show Answer
Answer:
Correct Answer: B
Solution:
$ y^{2}=(1-x^{2}) $
Therefore $ 2y\frac{dy}{dx}=-2x $ or $ \frac{dy}{dx}=\frac{-x}{y}=\frac{-xy}{(1-x^{2})} $
or $ (1-x^{2})\frac{dy}{dx}+xy=0 $ .
BETA
