calculus

If d/dx(f(x))=g(x) and d/dx(g(x))=f(x^2) , then d^2/dx^2(f(x^3))
, then d2dx2(f(x3))=

A f(x^6)
B g(x^3)
C 3x^2g(x^3)
D 9x^4f(x^6) + 6xg(x^3)
E f(x^6) + g(x^3)

I understood what the first half of the question said, but then I was confused by what the second half says. I'm confused on how to proceed with this question :(

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  1. d/dx f(x^3) = df/dx * 3x^2
    so,
    d^2/dx^2 f(x^3) = d/dx (d/dx f(x^3))
    = d/dx (df/dx * 3x^2)
    = d/dx (df/dx)) * 3x^2 + 6x df/dx
    It's beginning to look like D, right?

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    oobleck

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