Unless you have the Base Package of Labview, there should be a peak detector VI under Analyze -> Signal Processing -> Time Domain. That basically does exactly, what you want to do.
If you do not have that your idea to go back to calculus is good. If you have your data in as arrays of X and corresponding F(X) values you can calculate the derivative using a FOR loop and the following formula:
F'(Xn) = (F(X(n+1))-F(Xn))/(X(n+1)-Xn)
It is just an approximation, but it should work for your purposes.
Please see attached file for example.