Differentiation Question 370
Question: $ \frac{d}{dx}{{\tan }^{-1}}[ \frac{3a^{2}x-x^{3}}{a(a^{2}-3x^{2})} ] $ at $ x=0 $ is
Options:
A) $ \frac{1}{a} $
B) $ \frac{3}{a} $
C) $ 3a $
D) 3
Show Answer
Answer:
Correct Answer: B
Solution:
$ \frac{d}{dx}{{\tan }^{-1}}[ \frac{3a^{2}x-x^{3}}{a(a^{2}-3x^{2})} ] $
Put $ x=a\tan \theta $
$ \Rightarrow \frac{d}{dx}{{\tan }^{-1}}[ \frac{3a^{3}\tan \theta -a^{3}{{\tan }^{3}}\theta }{a^{3}-3a^{3}{{\tan }^{2}}\theta } ] $
$ =\frac{d}{dx}{{\tan }^{-1}}(\tan 3\theta )=\frac{d}{dx}(3\theta )=\frac{3a}{x^{2}+a^{2}} $
If $ x=0, $ then $ \frac{d}{dx}{{\tan }^{-1}}[ \frac{3a^{2}x-x^{3}}{a(a^{2}-3x^{2})} ]=\frac{3}{a} $ .
BETA
