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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?

user160601
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    People are often a bit sloppy about notation, but if we're being very careful then $f$ refers to a function whereas $f(x)$ refers to a number -- the number $f$ returns as output when it receives the number $x$ as input. If we try to make that distinction, then $y = f(x)$ implies that $y$ is a number rather than a function. If we intend for $y$ to be a function, we could simply say $y = f$. However, it then seems unnecessary to introduce $y$. – littleO Jun 28 '14 at 12:10

2 Answers2

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

beep-boop
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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 $${dy\over dx} = f'(x) = y'$$

user155312
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  • Newton's Notation is actually being used at my university, in the mechanics courses (I guess that's related to the fact that they're teaching Newtonian mechanics. – user160601 Jun 28 '14 at 13:37