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

Mar 9, 2016

$f ' \left(x\right) = 3 \left({x}^{2} + 1\right) \left(x - 3\right) + 6 x {\left(x - 3\right)}^{2}$
The product rule sates that $\frac{d}{\mathrm{dx}} \left[f \left(x\right) \cdot g \left(x\right)\right] = f \left(x\right) \cdot g ' \left(x\right) + g \left(x\right) \cdot f ' \left(x\right)$
$f ' \left(x\right) = \left({x}^{2} + 1\right) \cdot 3 \left(x - 3\right) + 3 {\left(x - 3\right)}^{2} \cdot 2 x$