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

Jul 6, 2015

I found: $20 x \left(2 - {x}^{3}\right) \left(1 - 2 {x}^{3}\right)$
I would use the Product Rule and the Chain Rule to deal with ${\left(\right)}^{2}$, and get:
$y ' = 10 x {\left(2 - {x}^{3}\right)}^{2} + 5 {x}^{2} \cdot 2 \left(2 - {x}^{3}\right) \cdot \left(- 3 {x}^{2}\right) =$
$= 10 x {\left(2 - {x}^{3}\right)}^{2} - 30 {x}^{4} \left(2 - {x}^{3}\right) =$
$= 10 x \left(2 - {x}^{3}\right) \left[2 - {x}^{3} - 3 {x}^{3}\right] =$
$= 10 x \left(2 - {x}^{3}\right) \left[2 - 4 {x}^{3}\right] = 20 x \left(2 - {x}^{3}\right) \left(1 - 2 {x}^{3}\right)$