JEE Main & Advanced
Mathematics
Applications of Derivatives
Question Bank
Critical Thinking
question_answer
The derivative of \[{{\tan }^{-1}}\left( \frac{\sqrt{1+{{x}^{2}}}-1}{x} \right)\]with respect to \[{{\tan }^{-1}}\left( \frac{2x\sqrt{1-{{x}^{2}}}}{1-2{{x}^{2}}} \right)\]at \[x=0\], is
A)\[\frac{1}{8}\]
B)\[\frac{1}{4}\]
C)\[\frac{1}{2}\]
D)1
Correct Answer:
B
Solution :
Let \[y={{\tan }^{-1}}\left( \frac{\sqrt{1+{{x}^{2}}}-1}{x} \right)\], \[z={{\tan }^{-1}}\left( \frac{2x\,\sqrt{1-{{x}^{2}}}}{1-2{{x}^{2}}} \right)\]