The differential of ln f(x) is f'(x)/f(x). For a function of the form y=ln (mx), the differential will always be 1/x. So ln (x/2) differentiated is 1/x and so is ln (4x/3).

To differentiate something like ax^b, multiply by the power, then take one off the power. So, the differential of 4x³ would be 12x².

To recap, y = ln (x/2), dy/dx = 1/x

y = 4x³ - ln (4x/3), dy/dx = 12x² - 1/x