Question

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

Answer 1

`f'(x)=2x^2(3x^3-10x+15).`

Explanation:

`f(x)=x^3(x^3-5x+10)=x^6-5x^4+10x^3.`

Knowing that, `(x^n)'=n*x^(n-1),` we have,

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

`=6*x^(6-1)-5(x^4)'+10(x^3)'`

`=6x^5-5(4x^3)+10(3x^2)`

`rArr f'(x)=6x^5-20x^3+30x^2=2x^2(3x^3-10x+15).`