Verified answer

Work from the outside in:

d/dx[f(1/x)]=x²

f(1/x) = 1/3 x^3

f(x) = 1/3 x^-3

f'(x) = -x^-4

f'(1/x) = -x^4

The answer is -x^4

You can also do this by noting that with the Chain Rule:

d/dx[f(1/x)] = d/dx(1/x) * f'(1/x) = -1/x^2 * f'(1/x) = x^2

Therefore f'(1/x) = -x^4