I encounter some problems with understanding the explanation of the follwing problem:
For which value of $\alpha$ does the graph of $f_\alpha(x)=e^{\alpha x}$ intersect the graph of $g(x) = \sqrt{x+1}$ orthogonally in the point $(0,1)$?
Normally, in this kind of problem, I would calculate both derivatives and equal them with the tangent of the angle, but $\tan(90^\circ)$ is not defined. In the explanation they are using $f'(0) \cdot g'(0) = -1$, but I don't understand how they obtained it. Is there a formula that I forgot?
