Differentiation Question 394
Question: $ \frac{d}{dx}{{\sin }^{-1}}(2ax\sqrt{1-a^{2}x^{2}})= $
Options:
A) $ \frac{2a}{\sqrt{a^{2}-x^{2}}} $
B) $ \frac{a}{\sqrt{a^{2}-x^{2}}} $
C) $ \frac{2a}{\sqrt{1-a^{2}x^{2}}} $
D) $ \frac{a}{\sqrt{1-a^{2}x^{2}}} $
Show Answer
Answer:
Correct Answer: C
Solution:
$ \frac{d}{dx}{{\sin }^{-1}}(2ax\sqrt{1-a^{2}x^{2}}) $
Putting $ ax=\sin \theta , $ we get $ =\frac{d}{dx}{{\sin }^{-1}}[2\sin \theta \sqrt{1-{{\sin }^{2}}\theta }]=\frac{d}{dx}{{\sin }^{-1}}\sin 2\theta =\frac{2a}{\sqrt{1-a^{2}x^{2}}} $
BETA
