Differentiate the following equation,
$(1 + x^{2}) c o s x$

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Solution

We have,
$\frac{d}{d x} ((1 + x^{2}) c o s x)$
$= c o s x \frac{d}{d x} (1 + x^{2}) + (1 + x^{2}) \frac{d}{d x} (c o s x)$ [Using product rule]
$= c o s x \times 2 x + (1 + x^{2}) (- s i n x)$
$= 2 x c o s x - (1 + x^{2}) s i n x$

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