# Please tell me what's the derivate of (2x^3-1)^4 ?

May 30, 2018

$24 {x}^{2} {\left(2 {x}^{3} - 1\right)}^{3}$

#### Explanation:

Using the power rule,
Bring the power down
Minus the power by one
Then multiply by the derivative by $\left(2 {x}^{3} - 1\right)$
$\frac{\mathrm{dy}}{\mathrm{dx}} = 4 {\left(2 {x}^{3} - 1\right)}^{4 - 1} \left(6 {x}^{2}\right)$
$= 24 {x}^{2} {\left(2 {x}^{3} - 1\right)}^{3}$

May 30, 2018

$24 {x}^{2} {\left(2 {x}^{3} - 1\right)}^{3}$

#### Explanation:

$\text{differentiate using the "color(blue)"chain rule}$

$\text{given "y=f(g(x))" then}$

$\frac{\mathrm{dy}}{\mathrm{dx}} = f ' \left(g \left(x\right)\right) \times g ' \left(x\right) \leftarrow \textcolor{b l u e}{\text{chain rule}}$

$\frac{d}{\mathrm{dx}} \left({\left(2 {x}^{3} - 1\right)}^{4}\right)$

$= 4 {\left(2 {x}^{3} - 1\right)}^{3} \times \frac{d}{\mathrm{dx}} \left(2 {x}^{3} - 1\right)$

$= 4 {\left(2 {x}^{3} - 1\right)}^{3} \times 6 {x}^{2}$

$= 24 {x}^{2} {\left(2 {x}^{3} - 1\right)}^{3}$