Differentiate the function with respect to $x$
$sin (x^{2} + 5)$

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Solution

Let $f (x) = sin (x^{2} + 5)$
Thus using chain rule,
$f^{'} (x) = \frac{d}{d x} (sin (x^{2} + 5)) \cdot \frac{d}{d x} (x^{2} + 5)$
$= cos (x^{2} + 5) \cdot 2 x = 2 x cos (x^{2} + 5)$

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