differentiate with respect to x. i). x^(1/2) ln (3x),

From this we can see that equation has 2 parts therefore we should look to using the product rule which is used to differiantiate a two functions multiplied together so (fg)'=f'g+fg'. In this question the differential of x^(1/2) is simply 1/2x^1/2 which can be rearranged using indices rules to 1/2x^1/2. Differentiating ln(3x) requires product rule in its own respect one can denote (3x) as U the ln(U) would simply be 1/U using ln then differential of u is 3. Therefore the differential on ln(3x) is 1/x simplified.
Overall the answer should ln(3x)/2x^(1/2) + 1/x^(1/2)