Derivative of sin^2(x)

Derivative of sin^2(x)

$\displaystyle y=\sin^2 \left( x \right)$

Put $\displaystyle u=\sin \left( x \right)$ ⇒ $\displaystyle u^2 = \sin^2 \left( x \right)$

$\displaystyle y=u^2$

$\displaystyle y'=(u^2)'$

$\displaystyle y'=2u*u'$

$\displaystyle u'=(sin(x))' = cos(x)$

$\displaystyle y'(x)=2sin(x)*cos(x)=sin2x$