Find the derivative with respect to $^{'} x^{'}$ of the function ${sin}^{- 1} (2 x)$ at $x = \frac{π}{4}$

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Solution

$f (x) = {sin}^{- 1} 2 x$
$f^{'} (x) = \frac{1}{\sqrt{1 - (2 x)^{2}}} \frac{d}{d x} (2 x)$
$= \frac{2}{\sqrt{1 - 4 x^{2}}}$
$a t x = \frac{π}{4} f^{'} (π / 4) = \frac{2}{\sqrt{1 + 4 {(\frac{π}{4})}^{2}}} = \frac{4}{\sqrt{4 + π^{2}}}$

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