# How do you find the derivative of f(x)=x^3(x^3-5x+10)?

Jun 22, 2017

$f ' \left(x\right) = 2 {x}^{2} \left(3 {x}^{3} - 10 x + 15\right) .$

#### Explanation:

$f \left(x\right) = {x}^{3} \left({x}^{3} - 5 x + 10\right) = {x}^{6} - 5 {x}^{4} + 10 {x}^{3.}$

Knowing that, $\left({x}^{n}\right) ' = n \cdot {x}^{n - 1} ,$ we have,

f'(x)=(x^6)'-(5x^4)'+(10x^3)'#

$= 6 \cdot {x}^{6 - 1} - 5 \left({x}^{4}\right) ' + 10 \left({x}^{3}\right) '$

$= 6 {x}^{5} - 5 \left(4 {x}^{3}\right) + 10 \left(3 {x}^{2}\right)$

$\Rightarrow f ' \left(x\right) = 6 {x}^{5} - 20 {x}^{3} + 30 {x}^{2} = 2 {x}^{2} \left(3 {x}^{3} - 10 x + 15\right) .$