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,
$f^{\prime}(x)=\left(5 x^{3}+3 x-1\right) \frac{d}{d x}(x-1) + (x-1) \frac{d}{d x}\left(5 x^{3}+3 x+1\right)$
$= (5x^3+ 3x − 1) \times 1 + (x − 1) \times (15x^2+ 3)$
$= (5x^3+ 3x − 1) + (x − 1) \times (15x^2+ 3)$
$= 5x^3+ 3x − 1 + 15x^3 + 3x − 15x^2 − 3$
$= 20x^3 - 15x^2 + 6x - 4$

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