How do I find a second derivative using a complex logarithm?

Answer by  therealscl (59)

First, you have an equation. You may use logarithmic differentiation if needed. Otherwsie it will suffice to use the usual definition (d/dx [ln x] = 1/x). Either take the log of both sides then differentiate, or differentiate directly. Then you have the first derivative. Repeat the action on this derivative.

Answer by  willard (874)

You can't. You can take the second derivative of a complex exponential, like e^{ikx}, the same way you would take the second derivative of a real exponential, e^{ax}.