How to prove jk=e^j-k using functions and perpendicular tangents

Question

The graphs of the functions f(x)=e^kx and g(x) = e^-jx have tangents which are perpendicular to each other when x=1. Prove hat jk=e^j-k.

I tried doing this question and thought i was doing well until I got my final answer as e^j-k = 1/jk and I'm not sure what I did wrong to get the answer wrong.

Answer 1

f'(x) = ke^kx; g'(x) = -je^-jx;f'(1) =ke^kl g'(1) = -je^-j; f'(1)g'(1) = -1 because of perpendicularity tangents.

So, ke^k(-je^-j) = -1; kj = e^j-k