Differentiation Question 53
Question: Differential coefficient of $ {{\cos }^{-1}}(\sqrt{x}) $ with respect to $ \sqrt{(1-x)} $ is
[MP PET 1997]
Options:
A) $ \sqrt{x} $
B) $ -\sqrt{x} $
C) $ \frac{1}{\sqrt{x}} $
D) $ -\frac{1}{\sqrt{x}} $
Show Answer
Answer:
Correct Answer: C
Solution:
Let $ y={{\cos }^{-1}}\sqrt{x} $ and $ z=\sqrt{1-x} $
$ \therefore \frac{dy}{dz}=\frac{\frac{-1}{\sqrt{1-x}}\times \frac{1}{2\sqrt{x}}}{-\frac{1}{2\sqrt{1-x}}}=\frac{1}{\sqrt{x}} $ .
BETA
