A) \[\frac{2-4{{x}^{2}}}{\sqrt{1-{{x}^{2}}}}\]
B) \[\frac{2+4{{x}^{2}}}{\sqrt{1-{{x}^{2}}}}\]
C) \[\frac{2-4{{x}^{2}}}{\sqrt{1+{{x}^{2}}}}\]
D) \[\frac{2+4{{x}^{2}}}{\sqrt{1+{{x}^{2}}}}\]
Correct Answer: A
Solution :
Let \[x=\sin \theta \Rightarrow 2{{\sin }^{-1}}x=2\theta \]Þ \[y=\sin 2\theta \] Þ\[\frac{dy}{dx}=\frac{dy/d\theta }{dx/d\theta }=\frac{2\cos 2\theta }{\cos \theta }\]\[=\frac{2(1-2{{\sin }^{2}}\theta )}{\sqrt{1-{{\sin }^{2}}\theta }}=\frac{2-4{{x}^{2}}}{\sqrt{1-{{x}^{2}}}}\].
You need to login to perform this action.
You will be redirected in
3 sec
