I've got this chain rule problem and I want to make sure I understand the solution entirely.

7/(x^{3 }+3x)^{1/3}

I rewrite and apply the chain rule: 7 d/dx -1/3(x^{3}+ 3x)^{-4/3}* (3x + 3)

My book has the answer as -7(x^2 + 1) / x^3 + 3x^{4/3}

I just wanted to get an experts opinion on the simplification. Did they just use the 3 in the denominator of -1/3 to cancel out the 3's in the last part of the expression? (3x + 3). So, they factored out a 3 on the last expression and that 3 canceled out the 3 in the -1/3?

Thank you all in advance for any input!