Differentiate x^2 ln(3x) with respect to x

This question requires the use of differentiation by product rule. First differentiate the first term, whilst keeping the second term the same, i.e. we get 2xln(3x). Secondly we keep the first term the same, and differentiate the second term, meaning it becomes x²(1/x), and thus our overall answer would be adding both of the things we got up (as that's the product rule). Thus the answer would be 2xln(3x) + x.