The derivative of f(x) = ln(2x) can be found using the chain rule. Let u = 2x and v = ln(u). Then, we have f(x) = v. Now, we can find the derivative of v with respect to u using the inverse function rule for logarithms: dv/du = 1/u. Next, we can find the derivative of u with respect to x: du/dx = 2. Finally, we can use the chain rule to find the derivative of f(x) with respect to x: df/dx = (dv/du) * (du/dx) = (1/u) * 2 = 2/u = 2/(2x) = 1/x Therefore, the derivative of f(x) = ln(2x) with respect to x is f'(x) = 1/x.
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