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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

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