It depends if you mean
[tex]f(x) = \sin(x^2+2x-1)^2 = \sin^2(x^2+2x-1)[/tex]
i.e. the sine part is getting squared, or
[tex]f(x) = \sin(x^2+2x-1)^2 = \sin\left((x^2+2x-1)^2\right)[/tex]
i.e. the argument to sine is getting squared. I'll assume the first case, since it's fairly common convention to write [tex]g(x)^2 = \bigg(g(x)\bigg)^2[/tex].
Now if
[tex]f(x) = \sin^2(x^2+2x-1)[/tex]
• by the power and chain rules we have
[tex]f'(x) = 2 \sin(x^2 + 2x - 1) \left(\sin(x^2+2x-1)\right)'[/tex]
• using the derivative of sine and the chain rule again we have
[tex]f'(x) = 2 \sin(x^2+2x-1) \cos(x^2+2x-1) \left(x^2+2x-1\right)'[/tex]
• with the power and chain rules we have
[tex]f'(x) = 2 \sin(x^2+2x-1) \cos(x^2+2x-1) (2x+2)[/tex]
Recalling the double angle identity for sine,
[tex]\sin(2x) = \sin(x) \cos(x)[/tex]
we can rewrite the derivative among several other ways as
[tex]\boxed{f'(x) = (2x+2) \sin(2x^2+4x-2)}[/tex]
