Thread: the chain rule

I have 2 questions

1) y=sin(x^2) = 2X cos(x^2)

which i sort of understand but not shure how to do

2) y= (sinx)^2 cn someone explain the answer ?

It's like when differentiating $\displaystyle x^n,$ in this case our $\displaystyle x$ is $\displaystyle \sin x,$ hence, we require to apply the chain rule (actually, when one differentiates $\displaystyle x^n$ is applyin' the chain rule, it's just that $\displaystyle (x)'=1$), hence $\displaystyle y'=2\sin(x)\cdot(\sin x)'.$