Differentiate the following functions with respect to x:
$(x^{3} + x^{2} + 1) s i n x$

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Solution

We have,

$\frac{d}{d x} (x^{3} + x^{2} + 1) s i n x$

$= s i n x \frac{d}{d x} (x^{3} + x^{2} + 1) + (x^{3} + x^{2} + 1)$

$\frac{d}{d x} (s i n x)$ [Using product rule]

$= s i n x (3 x^{2} + 2 x) + (x^{3} + x^{2} + 1) c o s x$

$∴ (x^{3} + x^{2} + 1) c o s x + 1 (3 x^{2} + 2 x) s i n x$

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