# Notation for Derivatives with Respect to Time

My math teacher writes $\frac{dx}{dt}$ as $x'$, and makes us do the same for homework. (in a particle motion context, where $t$ is time)

I am aware that the standard notation is usually $\dot{x}$, and I have never seen the teacher's notation in textbooks. However, my teacher finds that dots are often impractical for handwriting (she says that sometimes the dot is too small to be seen or we have to press harder on the paper to make it obvious etc.)

My question is; would it be wrong to write the derivative with a prime?

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She definitely has a point with the dot being easily overlooked in handwriting. Though to be fair, one should shy away from using $u$ and $v$ in the same formula too, then - at least with my handwriting, they two are virtually indistinguishable... – fgp May 1 '14 at 9:31

No, it's not wrong. I think the prime is the usual way, and the dot is just a special way for time derivatives like you already said.

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Derivatives have many different notations.

The notation used by your teacher is known as Lagrange's notation ($y'$ or $f'$), using as many apexes as the degree of differentiation. However are also very popular Newton's notation ($\dot{y}$), using dots instead of apexes, Leibniz's notation written as fraction and using exponents for the degree of differentiation ($\frac{dy}{dt}$ or $\frac{d}{dt}f$, $\frac{d^2y}{dt^2}$ for the second derivative), and Euler's notation using exponents too ($D_ty$, $D^{2}_ty$)

Personally, I prefer Lagrange's and Leibniz's notations, but all of them are widely used and understood, and that is the point of a notation.

Also, you must take consideration of the context and the medium you are using: as your teacher pointed out, Newton's notation isn't a good option for handwriting, while a less concise notation would be a better choice (Leibniz's notation for example). In the same way, in particular mathematical contexts apexes could be ambiguous thus Lagrange's notation would be an equally bad choice.

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