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

Oct 27, 2015

$\frac{d}{\mathrm{dx}} x {\left({x}^{2} - 2 x + 1\right)}^{4} = \left(8 {x}^{2} - 8 x\right) {\left({x}^{2} - 2 x + 1\right)}^{3} + {\left({x}^{2} - 2 x + 1\right)}^{4}$
$\frac{d}{\mathrm{dx}} \left[f \left(x\right) \cdot g \left(x\right)\right] = f \left(x\right) \cdot g ' \left(x\right) + g \left(x\right) \cdot f ' \left(x\right)$
$\therefore \frac{d}{\mathrm{dx}} x {\left({x}^{2} - 2 x + 1\right)}^{4} = \left(x\right) \cdot 4 {\left({x}^{2} - 2 x + 1\right)}^{3} \left(2 x - 2\right) + {\left({x}^{2} - 2 x + 1\right)}^{4}$