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How do I fully differentiate (x^3+1)3(9-x^3)^1/3?

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How do I fully differentiate (x^3+1)3(9-x^3)^1/3?

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  1. dy/dx=(3x^3+3)[1/3(9-x^3)^-2/3(-3x^2)]+(...

             =(3x^3+3)(9-x^3)^1/3.x^2[-1(9-x^3)^1+9]

             =x^2(3x^3+3)(9-x^3)1/3.9/(9-x^3)

             =9x^2(3x^3+3)/(9-x^3)^2/3

    I think this should be the answer..if I were not mistaken in differentiating...

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