Differentiate sin - 12x-1 - x2

[ Let,x = cosθ; sin ^ 1(2cosθ√(1 cosθ ^2) ); #160;= sin ^ 1(2cosθsinθ ); #160;= sin ^ 1(2sinθ ); ...

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Derivative of Standard Functions

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Question

Differentiate ${sin}^{- 1} (2 x \sqrt{1 - x^{2}})$

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y = {s i n}^{- 1} (2 x \sqrt{1 - x^{2}})

{tan}^{- 1} (\frac{x}{\sqrt{1 - x^{2}}})

{sin}^{- 1} (2 x \sqrt{1 - x^{2}}) .

\tan^{- 1} (\frac{x}{\sqrt{1 - x^{2}}})

\sin^{- 1} (2 x \sqrt{1 - x^{2}}), if - \frac{1}{\sqrt{2}} < x < \frac{1}{\sqrt{2}}

x

y = {sin}^{- 1} (\frac{2 x}{1 + x^{2}})

{tan}^{- 1} (\frac{\sqrt{1 - x^{2}} - 1}{x})

{sin}^{- 1} (\frac{2 x}{1 + x^{2}})

x \neq 0.

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