Differentiate the following functions with respect to x :

$(2 x^{2} + 1) (3 x + 2)$

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Solution

We have,

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

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

[Using product rule]

$= (3 x + 2) (4 x + 0) + (2 x^{2} + 1) (3 + 0) .$

$= (12 x^{2} + 8 x + 6 x^{2} + 3)$

$= 18 x^{2} + 8 x + 3$

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