Find the derivative of (5 x^ 3 +3 x-1 )(x-1) - Vidyadip

Question

Find the derivative of
$\left(5 x^{3}+3 x-1\right)(x-1)$

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Answer

Let $f(x)=\left(5 x^3+3 x-1\right)(x-1)$
By product rule of differentiation,we have,
$f^{\prime}(x)=\left(5 x^3+3 x-1\right) \frac{d}{d x}(x-1)+(x-1) \frac{d}{d x}\left(5 x^3+3 x+1\right)$
$=\left(5 x^3+3 x-1\right) \times 1+(x-1) \times\left(15 x^2+3\right)$
$=\left(5 x^3+3 x-1\right)+(x-1) \times\left(15 x^2+3\right)$
$=5 x^3+3 x-1+15 x^3+3 x-15 x^2-3$
$=20 x^3-15 x^2+6 x-4$

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