#### Answer

$y'=8x^3sin(2x^2)cos(2x^2)+2xsin^2(2x^2)$

#### Work Step by Step

Take the derivative of the equation using Power Rule, Product Rule, Trigonometric derivative, and Chain Rule:
$y'=x^2\times2sin(2x^2)\times cos(2x^2)\times4x+2xsin^2(2x^2)$
$=8x^3sin(2x^2)cos(2x^2)+2xsin^2(2x^2)$