Derivative of ln(x)

Differentiating ln(x) is a single-rule problem: everything follows from the natural log rule. That makes it a good expression for isolating and practicing that one technique.

The natural logarithm differentiates to the reciprocal: d/dx[ln x] = 1/x. When the argument of the log is itself a function, the chain rule divides its derivative by that argument.

A good way to verify a derivative by hand is to compare it against the step-by-step breakdown above — each step names the rule being applied, so you can pinpoint exactly where your own work diverges if the answers differ.