How do you differentiate f(x)=(2x^2+1)(2x-1) using the product rule?

Dec 24, 2015

$f ' \left(x\right) = 2 \left(2 {x}^{2} + 1\right) + 4 x \left(2 x - 1\right)$

$= 12 {x}^{2} - 4 x + 2$

Explanation:

Product rule states that $\frac{d}{\mathrm{dx}} \left(f \left(x\right) \cdot g \left(x\right)\right) = f \left(x\right) \cdot g ' \left(x\right) + g \left(x\right) \cdot f ' \left(x\right)$.

Application thereof in this particular case yields

$f ' \left(x\right) = 2 \left(2 {x}^{2} + 1\right) + 4 x \left(2 x - 1\right)$