differentiation

Question: If $y={{\tan }^{-1}}\frac{x}{1+\sqrt{1-{{x}^{2}}}}+\sin \left\{ 2{{\tan }^{-1}}\sqrt{\left( \frac{1-x}{1+x} \right)} \right\}$,then $\frac{dy}{dx}$=

1) $\frac{x}{\sqrt{1-{{x}^{2}}}}$

2) $\frac{1-2x}{\sqrt{1-{{x}^{2}}}}$

3) $\frac{1-2x}{2\sqrt{1-{{x}^{2}}}}$

4) $\frac{1}{1+{{x}^{2}}}$

Solution:

Explanation: No Explanation

Differentiation by substitution Higher order derivatives

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