Differentiation Question 115
Question: Differential coefficient of $ {{\sin }^{-1}}x $ w.r.t $ {{\cos }^{-1}}\sqrt{1-x^{2}} $ is
[MNR 1983; AMU 2002]
Options:
A) 1
B) $ \frac{1}{1+x^{2}} $
C) 2
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
Let $ y_1={{\sin }^{-1}}x $ and $ y_2={{\cos }^{-1}}\sqrt{1-x^{2}} $
Differentiating w.r.t. x of $ y_1 $ and $ y_2 $ , we get $ \frac{dy_1}{dx}=\frac{1}{\sqrt{1-x^{2}}} $
$ \frac{dy_2}{dx}=-\frac{1}{\sqrt{1-(1-x^{2})}}\frac{1(-2x)}{2\sqrt{1-x}}=\frac{1}{\sqrt{1-x^{2}}}\Rightarrow \frac{dy_2}{dy_1}=1. $
BETA
