Differentiate 7(3x^2+7)^(1/3)

Begin by differentiating the terms in the brackets, which gives just 6x. Bring 6x forward, out of the brackets, together with the index on the brackets - 1/3. This gives 42x/3 or 14x in front of the brackets. Decrease the index by 1 and leave the contents of the brackets as they are to get 14x(3x^2+7)^(-2/3).