Question

f(x) = (5x³+3x-1) (x - 1) by produet Rule of differentiation ​

Answer 1

Step-by-step explanation:

We have,

$f(x) = (5 {x}^{3} + 3x - 1)(x - 1)$

$\implies \: f^{'}(x) = (x - 1).\frac{d}{dx} (5 {x}^{3} + 3x - 1) + (5 {x}^{3} + 3x - 1). \frac{d}{dx} (x - 1)$

$\implies \: f^{'}(x) = (x - 1)(15 {x}^{2} + 3) + (5 {x}^{3} + 3x - 1)(1)$

$\implies \: f^{'}(x) = 15 {x}^{3} - 15 {x}^{2} + 3x - 3 + 5 {x}^{3} + 3x - 1$

$\implies \: f^{'}(x) = 20 {x}^{3} - 15 {x}^{2} + 6x - 4$