Differentiate the following w.r.t. $x$ .
$(3 x^{2} + 2) (4 x - 3 x^{3})$ .

45 x^{4} + 18 x^{2} + 8

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- 45 x^{4} + 18 x^{2} + 8

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- 45 x^{4} + 15 x^{2} + 8

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- 45 x^{4} + 18 x^{2} + 18

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Solution

The correct option is C $- 45 x^{4} + 18 x^{2} + 8$
$D = \frac{d}{d x} (3 x^{2} + 2) (4 x - 3 x^{3})$
Using multiplication rule,
$D = (4 x - 3 x^{3}) \frac{d}{d x} (3 x^{2} + 2) + (3 x^{2} + 2) (\frac{d}{d x} (4 x - 3 x^{3}))$
$= (4 x - 3 x^{3}) . (6 x) + (3 x^{2} + 2) (4 - 9 x^{2})$
$= 24 x^{2} - 18 x^{4} + 12 x^{2} - 27 x^{4} + 8 - 18 x^{2}$
$= - 45 x^{4} + 18 x^{2} + 8$

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