Differentiation Question 89
Question: Differential coefficient of $ {{\sin }^{-1}}\frac{1-x}{1+x}w.r.t $
$ \sqrt{x} $ is
[Roorkee 1984]
Options:
A) $ \frac{1}{2\sqrt{x}} $
B) $ \frac{\sqrt{x}}{\sqrt{1-x}} $
C) 1
D) None of these
Show Answer
Answer:
Correct Answer: D
Solution:
Let $ y={{\sin }^{-1}}\frac{1-x}{1+x} $
Therefore $ \frac{dy}{dx}=\frac{-1}{\sqrt{x}(1+x)} $ ….(i) and $ z=\sqrt{x} $
Therefore $ \frac{dz}{dx}=\frac{1}{2\sqrt{x}} $
…..(ii) Therefore by (i) and (ii) $ \frac{dy}{dz}=\frac{dy/dx}{dz/dx}=\frac{-2}{1+x} $ .
BETA
