Derivative of a function evaluated at some point

Question

I just want to be sure about this:

If I have a differentiable function $f(x)$, then $f'(p)$ (or the nth derivative of f at $p$),which $p$ is where the nth derivative is being evaluated, should I consider $f'(p)$ as a constant or not?

Also, does it differ when I do not know exactly the value of $p$? I mean, I'm just sure that $p$ is a point where $f$ is defined.

Thanks

Answer 1

The derivative of a function at a point by definition is the slope of the line tangent to the curve at the point. Then if $ p $ is a constant $ f'(p) $ is also a constant.