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) \[\frac{a}{\sqrt{1-{{a}^{2}}{{x}^{2}}}}\]
Correct Answer: C
Solution :
\[\frac{d}{dx}{{\sin }^{-1}}(2ax\sqrt{1-{{a}^{2}}{{x}^{2}}})\] Putting \[ax=\sin \theta ,\]we get \[=\frac{d}{dx}{{\sin }^{-1}}[2\sin \theta \sqrt{1-{{\sin }^{2}}\theta }]=\frac{d}{dx}{{\sin }^{-1}}\sin 2\theta =\frac{2a}{\sqrt{1-{{a}^{2}}{{x}^{2}}}}\]
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