Find the derivative of the following wrt to x using chain rule
$\sqrt[3]{s i n 2 x}$

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Solution

$\frac{d}{d n} (s i n 2 x)^{\frac{1}{3}} = \frac{1}{3} (s i n 2 x)^{\frac{1}{3} - 1} \times \frac{d}{d n} (s i n 2 x) = \frac{1}{3} (s i n 2 x)^{- \frac{2}{3}} (c o s 2 x) \times \frac{d}{d n} (2 x) = \frac{1}{3} (s i n 2 x)^{- \frac{2}{3}} (c o s 2 x) (2) = \frac{2}{3} (s i n 2 x)^{- \frac{2}{3}} c o s 2 x$

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