Question

How do you find the derivative of `5x^2(2-x^3)^2`?

Answer 1

I found: `20x(2-x^3)(1-2x^3)`

Explanation:

I would use the Product Rule and the Chain Rule to deal with `()^2`, and get:
`y'=10x(2-x^3)^2+5x^2*2(2-x^3)*(-3x^2)=`
`=10x(2-x^3)^2-30x^4(2-x^3)=`
`=10x(2-x^3)[2-x^3-3x^3]=`
`=10x(2-x^3)[2-4x^3]=20x(2-x^3)(1-2x^3)`