Differentiate with respect to x: y = xln[2x]
This is an example of a question where we would have to use the product rule for differentiation, because we have two functions multiplied together ( x and ln(2x) ).If we have: y = uv, where u and v are functions of x then the product rule tells us that dy/dx = uv' + vu'. So, if u = x and v = ln[2x] then u' = 1 and v' = 1/x . Remember that the differential of ln(f(x)) = f'(x) / f(x)Then, applying the product rule, we have that dy/dx = (x) (1/x) + (ln(2x)) (1) = 1 + ln(2x) Our final answer is: 1 + ln(2x)
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