Differentiation Question 5
Question: Differential coefficient of $ \sqrt{\sec \sqrt{x}} $ is
[MP PET 1996]
Options:
A) $ \frac{1}{4\sqrt{x}}{{(\sec \sqrt{x})}^{3/2}}\sin \sqrt{x} $
B) $ \frac{1}{4\sqrt{x}}\sec \sqrt{x}\sin \sqrt{x} $
C) $ \frac{1}{2}\sqrt{x}{{(\sec \sqrt{x})}^{3/2}}\sin \sqrt{x} $
D) $ \frac{1}{2}\sqrt{x}\sec \sqrt{x}\sin \sqrt{x} $
Show Answer
Answer:
Correct Answer: A
Solution:
$ \frac{d}{dx}( \sqrt{\sec \sqrt{x}} )=\frac{1}{2\sqrt{\sec \sqrt{x}}}.\frac{d}{dx}(\sec \sqrt{x}) $
$ =\frac{1}{2{{(\sec \sqrt{x})}^{1/2}}}.\sec \sqrt{x}.\tan \sqrt{x}.\frac{1}{2\sqrt{x}} $
$ x^{2}=\cos 2\theta $ .
BETA
