Second derivative ln(2x), chain rule with natural log, then power rule. #shorts

Second derivative ln(2x), chain rule with natural log, then power rule.

We recognize ln(2x) as a function composition with 2x as the inner function and natural log as the outer function. We differentiate ln(2x) with respect to 2x, giving us 1/2x, then the chain rule requires that we multiply by the derivative of 2x which is 2. This results in a first derivative of 1/x, which we re-express as x^-1. When we apply the second derivative, we just use the power rule to obtain -1/x^2 for the final answer.