Find the derivative of the following:
$(5 x^{3} + 3 x - 1) (x - 1)$ .

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Solution

Let $f (x) = (5 x^{3} + 3 x - 1) (x - 1)$
Thus using product rule of differentiation,
$f^{^{'}} (x) = (5 x^{3} + 3 x - 1) \frac{d}{d x} (x - 1) + (x - 1) \frac{d}{d x} (5 x^{3} + 3 x - 1)$
$= (5 x^{3} + 3 x - 1) (1) + (x - 1) (5.3 x^{2} + 3 - 0)$
$= (5 x^{3} + 3 x - 1) + (x - 1) (15 x^{2} + 3)$
$= 5 x^{3} + 3 x - 1 + 15 x^{3} + 3 x - 15 x^{2} - 3$
$= 20 x^{3} - 15 x^{2} + 6 x - 4$

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