# How do you find the derivative of y = x^4(2x - 5)^6?

Oct 8, 2016

$y ' = u ' v + v ' u$- product rule

#### Explanation:

Let $u = {x}^{4}$ and $v = {\left(2 x - 5\right)}^{6}$
$u ' = 4 {x}^{3}$
$v ' = 2 \cdot 6 {\left(2 x - 5\right)}^{5} = 12 {\left(2 x - 5\right)}^{5} \to$by chain rule

Subbing into $y ' = u ' v + v ' u$,

$y ' = 4 {x}^{3} {\left(2 x - 5\right)}^{6} + 12 {\left(2 x - 5\right)}^{5} {x}^{4}$

Simplifying,

$y ' = {x}^{3} {\left(2 x - 5\right)}^{5} \left(4 \left(2 x - 5\right) + 12 x\right) = {x}^{3} {\left(2 x - 5\right)}^{5} \left(20 x - 20\right)$