The derivative of ln(x) is 1/x.
The derivative of ln(x) is equal to 1/x because ln(x) is the inverse of the natural logarithmic function e^x. Thus, the derivative of ln(x) is the inverse of the derivative of e^x, which is 1/x.
The general rule for finding the derivative of a natural log function, ln(x), is to take the inverse of the function inside the ln and multiply it by the derivative of the function inside the ln.
To find the derivative of ln(u), where u is a function of x, you must use the chain rule. Take the derivative of ln(u) as if u was a variable, and then multiply it by the derivative of u with respect to x.
The derivative of ln(f(x)) is 1/f(x) * f'(x), or simply f'(x)/f(x). This can also be written as (f(x))'/f(x), where (f(x))' is the derivative of f(x).