A simple ln differentiation question
I'm somewhat embarassed to be asking such a simple question but hopefully someone would be kind enough to help me out.
I've been asked to find the first and second derivatives of A = ln x so I got the following, which agreed with the answers given:
A' = 1/x
However, my confusion is with the second derivative. I prefer to use x^-1 rather than 1/x. Using x^-1 would give me -1*x^-1-1:
A'' = -x^-2 or -1/x^2
The answer given is 1/x^2 (ie positive, rather than the negative answer I get).
Would somebody be kind enough to tell me which is correct and, if I'm wrong, please explain where I've gone wrong. Thanks very much.