Differentiation Question 120
Question: $ \frac{d}{dx}{{\cos }^{-1}}\sqrt{\cos x}= $
Options:
A) $ \frac{1}{2}\sqrt{1+\sec x} $
B) $ \sqrt{1+\sec x} $
C) $ -\frac{1}{2}\sqrt{1+\sec x} $
D) $ -\sqrt{1+\sec x} $
Show Answer
Answer:
Correct Answer: A
Solution:
$ \frac{d}{dx}{{\cos }^{-1}}\sqrt{\cos x}=\frac{\sin x}{2\sqrt{\cos x}\sqrt{1-\cos x}} $
$ =\frac{\sqrt{1-{{\cos }^{2}}x}}{2\sqrt{\cos x}\sqrt{1-\cos x}}=\frac{1}{2}\sqrt{\frac{1+\cos x}{\cos x}} $ .
BETA
