Differentiate the following functions with respect to x.

$s i n (x^{2} + 5)$

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Solution

Let y = $s i n (x^{2} + 5)$

Differentiate both sides w.r.t. x, we get

$\frac{d y}{d x} = \frac{d}{d x} (s i n (x^{2} + 5)) = c o s (x^{2} + 5) \frac{d}{d x} (x^{2} + 5)$ (By using chain rule)

= $c o s (x^{2} + 5) (2 x + 0) = 2 x c o s (x^{2} + 5)$

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