# How do you differentiate f(x) = (x^2 + 6) (4x^6 + 5) using the product rule?

Oct 27, 2015

$\frac{d}{\mathrm{dx}} \left({x}^{2} + 6\right) \left(4 {x}^{6} + 5\right) = 24 {x}^{5} \left({x}^{2} + 6\right) + 2 x \left(4 {x}^{6} + 5\right)$

#### Explanation:

According to the product rule,
$\frac{d}{\mathrm{dx}} \left[f \left(x\right) \cdot g \left(x\right)\right] = f \left(x\right) \cdot g ' \left(x\right) + g \left(x\right) \cdot f ' \left(x\right)$

$\therefore \frac{d}{\mathrm{dx}} \left({x}^{2} + 6\right) \left(4 {x}^{6} + 5\right) = \left({x}^{2} + 6\right) \left(24 {x}^{5}\right) + \left(4 {x}^{6} + 5\right) \left(2 x\right)$