How to differentiate y=sin^2 (x)?

Question

answer is sin2x but i need the working

Answer 1

y = sin²(x)

u = sin(x)

y = u²

dy/du = 2u = 2sin(x)

u = sin(x)

du/dx = cos(x)

dy/dx

= (dy/du)(du/dx)

= 2sin(x)cos(x)

= sin(2x)

Answer 2

y      = sin^2(x)

dy/dx= d(sin^2(x))/dx

        = 2*sin^(2-1)(x)*d(sin(x))/dx   ---> Ref 1 (derivative of x^n = nx^(n-1))

        = 2*sin(x)*d(sin(x))/dx

        = 2*sin(x)*cos(x)

        = sin(x)*cos(x) + sin(x)*cos(x)

        = sin(x+x)           ---> Ref 2 (sin(A+B)=sin A cos B + cos A sin B)

        = sin(2x)