1

In highschool we had to write it like $f'(x)$. But isn't that the same as writing it as $\frac{d}{dx}f(x)$?

  • If nay, what is the difference?
  • If yay, why did we wrote it like that in highschool?
J. W. Tanner
  • 60,406
  • 4
    It's the same, indeed. – xyz Jun 01 '21 at 16:36
  • 2
    They are the same thing. The former is Newton's notation, the latter Leibniz's. – Ritam_Dasgupta Jun 01 '21 at 16:37
  • Perhaps interesting: https://hsm.stackexchange.com/questions/55/what-is-the-difference-between-calculus-of-newton-and-that-of-leibniz#:~:text=Newton%27s%20calculus%20is%20about%20functions,limit%20is%20a%20separate%20operation. – vitamin d Jun 01 '21 at 16:45
  • 1
    Historically, people would write $\frac{df(x)}{dx}$ to mean $$\frac{f(x+dx)-f(x)}{dx} , ,$$where $dx$ was an 'infinitely small' non-zero number. Because such numbers don't exist in the real number system, nowadays people typically interpret $\frac{d}{dx}f(x)$ as the limit $$\lim_{h \to 0}\frac{f(x+h)-f(x)}{h} , ,$$or as the result of applying the derivative operator $\frac{d}{dx}$ to $f(x)$. Regardless of your interpretation, $\frac{d}{dx}f(x)=f'(x)$ always. – Joe Jun 01 '21 at 16:45
  • The difference is just of notation – Lalit Tolani Jun 01 '21 at 16:49
  • In calculus (university) we still used $f'(x)$ we only used $d/dx f(x) $ in differential equations. – kingW3 Jun 01 '21 at 17:02
  • If there is a difference, it's purely aesthetic. For example, I think expressing the derivative at a point is better served by the "prime" notation, $f'(c)$, as opposed to, say, $\frac{\mathrm df}{\mathrm dx}\big|_{x=c}$. – user170231 Jun 01 '21 at 17:11
  • There is no difference. However, the "$\frac{df}{dx}$ notation" is very useful if your function $f$ has more than one variable. The partial derivatives of, say, a function $f(x,y)$ are written as $\frac{\partial f}{\partial x}$ and $\frac{\partial f}{\partial y}$. – Paul Frost Sep 02 '21 at 23:48

1 Answers1

2

They are the same. We use the $f'(x)$ or more generally $f^{(n)}(x)$ to save space.

:)

Young Kindaichi
  • 516