# How do you differentiate y=x²(2x+5)³?

Jan 7, 2016

Product rule states that for $y = f \left(x\right) g \left(x\right)$, then $\frac{\mathrm{dy}}{\mathrm{dx}} = f ' \left(x\right) g \left(x\right) + f \left(x\right) g ' \left(x\right)$

#### Explanation:

In this case, we'll also need the chain rule to differentiate the second term.

Chain rule: $\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{\mathrm{dy}}{\mathrm{du}} \frac{\mathrm{du}}{\mathrm{dx}}$

$\frac{\mathrm{dy}}{\mathrm{dx}} = 2 x {\left(2 x + 5\right)}^{3} + {x}^{2} \left(3 {\left(2 x + 5\right)}^{2} \left(2\right)\right)$

$\frac{\mathrm{dy}}{\mathrm{dx}} = 2 x {\left(2 x + 5\right)}^{2} \left(\left(2 x + 5\right) + 3 x\right)$