Is $y'$ a valid notation for $f'(x)$?

Question

In this context, let us say that:

$$y=f(x)$$

I've seen both the notation $y'$ and $f'(x)$ being used. Are both correct?

Answer 1

Yes, both mean derivative of

Lagrange’s Notation is to write the derivative of the function $f(x)$ as $f'(x)$

Leibniz’s Notation is to write the derivative of the function $y$ as ${dy\over dx}$ or $y$ as $y'$

Some other uncommon notations are:

Euler's Notation for function $D$ as $Df$

Newton's Notation for function $y$ as: $\dot{y}$

In summary $${dy\over dx} = f'(x) = y'$$

Answer 2

Yes, that's fine, but if you want to be absolutely unambiguous (about which variable you're differentiating $y$ with respect to), write $y'(x)$.