# How do you differentiate f(x)=(x^2+4x)*(x^3+2x+1) using the product rule?

Dec 31, 2015

Product rule states that for $y = f \left(x\right) g \left(x\right)$, then $\frac{\mathrm{dy}}{\mathrm{dx}} = f ' \left(x\right) g \left(x\right) + f \left(x\right) g ' \left(x\right)$.
$\frac{\mathrm{dy}}{\mathrm{dx}} = \left(2 x + 4\right) \left({x}^{3} + 2 x + 1\right) + \left({x}^{2} + 4 x\right) \left(3 {x}^{2} + 2\right)$
$\frac{\mathrm{dy}}{\mathrm{dx}} = \left(2 {x}^{4} + 4 {x}^{3} + 4 {x}^{2} + 10 x + 4\right) + \left(3 {x}^{4} + 12 {x}^{3} + 2 {x}^{2} + 8 x\right)$
$\frac{\mathrm{dy}}{\mathrm{dx}} = 5 {x}^{4} + 16 {x}^{3} + 6 {x}^{2} + 18 x + 4$