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

Mar 9, 2016

#### Answer:

$f ' \left(x\right) = 3 \left({x}^{2} + 1\right) \left(x - 3\right) + 6 x {\left(x - 3\right)}^{2}$

#### Explanation:

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

Thus in the given example, we need the power rule for the second factor, and get

$f ' \left(x\right) = \left({x}^{2} + 1\right) \cdot 3 \left(x - 3\right) + 3 {\left(x - 3\right)}^{2} \cdot 2 x$