Derivative of (ln(x))/2: Step-by-Step Guide

To find the derivative of (ln(x))/2, we can use the quotient rule.

The quotient rule states that if we have a function f(x) = g(x)/h(x), then the derivative of f(x) is given by:

f'(x) = (g'(x) * h(x) - g(x) * h'(x))/[h(x)]^2

In this case, g(x) = ln(x) and h(x) = 2. Since h(x) is a constant, its derivative is 0.

g'(x) is the derivative of ln(x), which is 1/x.

Using the quotient rule, we can find the derivative of (ln(x))/2 as follows:

f'(x) = (1/x * 2 - ln(x) * 0)/[2]^2 = 2/x^2

Therefore, the derivative of (ln(x))/2 is 2/x^2.