ok so you have sin(pi^2*x^2)

find the derivative of sin while keeping everything else inside the parenthesis the same, so:

cos(pi^2*x^2)

Next, use the chain rule on x^2

and you will get your answer of cos(pi^2*x^2) * 2(pi^2)*x

So, you start off with d/dx (sin(πx)^2)

Turn that into:

cos(π^2 x^2)*d/dx (π^2 x^2)

Which is:

π^2 * d/dx(x^2) * cos(π^2 x^2)

Hence:

2π^2*x*cos(π^2 x^2)

i) y = sin u, y' = u' * cosu

ii)

f(x) = u^n , f'(x) = n * u' * u^(n-1)

=>

f(x) = (πx)^2 , f'(x) = 2π(πx)^1 = 2xπ^2

i,ii) ==> d/dx = 2xπ^2 cos(xπ)^2