Find derivative of the following with respect to B:
$s i n^{- 1} (2 x \sqrt{1 - x^{2}}); - \frac{1}{\sqrt{2}} < x < \frac{1}{\sqrt{2}}$

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Solution

$\frac{d}{d x} s i n^{- 1} (2 x \sqrt{1 - x^{2}}) = \frac{1}{\sqrt{1 - 4 x^{2} (1 - x^{2})}} . \frac{d}{d x} (2 x \sqrt{1 - x^{2}}) = \frac{1}{\sqrt{1 - 4 x^{2} (1 - x^{2})}} [2 (1 - x^{2})^{1 / 2} + \frac{1}{2} 2 x (1 - x^{2})^{- 1 / 2}] = \frac{1}{\sqrt{1 - 4 x^{2} (1 - x^{2})}} [2 (1 - x^{2})^{1 / 2} + x (1 - x^{2})^{- 1 / 2}]$

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