Question

Differentiate (2x+1) (x³-1)​

Answer 1

Answer:

The answer is

$\frac{d}{dx} = 8 {x}^{3} + 3 {x}^{2} - 2$

Explanation:

You have to apply Product Rule,

$\frac{dy}{dx} = u \frac{dv}{dx} + v \frac{du}{dx}$

$let \: u = 2x + 1$

$\frac{du}{dx} = 2$

$let \: v = {x}^{3} - 1$

$\frac{dv}{dx} = 3 {x}^{2}$

Finally :

$\frac{d}{dx} = (2x + 1)(3 {x}^{2} ) + ( {x}^{3} - 1)(2)$

$\frac{d}{dx} = 6 {x}^{3} + 3 {x}^{2} + 2 {x}^{3} - 2$

$\frac{d}{dx} = 8{x}^{3} + 3 {x}^{2} - 2$