# What is the derivative of (4x)^3 * (2x)^6?

Nov 1, 2016

$y ' = 36864 {x}^{8}$

#### Explanation:

$y = {\left(4 x\right)}^{3} {\left(2 x\right)}^{6}$

$y = {4}^{3} {x}^{3} \cdot {2}^{6} {x}^{6}$

$y = 4096 {x}^{9}$

$y ' = 36864 {x}^{8}$

OR

Use product rule and chain rule

$f = {\left(4 x\right)}^{3} , g = {\left(2 x\right)}^{6}$

$f ' = 3 {\left(4 x\right)}^{2} \cdot 4 , g ' = 6 {\left(2 x\right)}^{5} \cdot 2$

$y ' = f g ' + g f '$

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

$y ' = 12 \cdot {4}^{3} {x}^{3} \cdot {2}^{5} {x}^{5} + 12 \cdot {4}^{2} {x}^{2} \cdot {2}^{6} {x}^{6}$

$y ' = 24576 {x}^{8} + 12288 {x}^{8} = 36864 {x}^{8}$