Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Assuming, naively, that one acquires the nth derivative of a function by repeatedly differentiating and finding a pattern. Thus one gets $f^{(n)}(x)=g(x,n)$. I have a few questions about this situation.

The first derivative at a point is the slope of the line tangent to the curve at the point. The second derivative measures the concavity of the graph of a function. Are there corresponding "explanations" for higher order derivatives?

The first integral measures the area between the curve and the x-axis. Are there similar "explanations" for higher integrals?

If one has the function $g(x,n)$, does it make sense to put a non-integer real number or imaginary number on the place of $n$? I know there exists a rigorous field of fractional calculus, but I know next to nothing about it.

If one has $g(x,n)$, when will $g(x,0)=f(x)$? How about when will $g(x,-1)=\int f(x) dx ?$

If one replaces $n$ in $g(x,n)$ with a fraction, one will get a proper function. What is this function, what does it "mean", does it have an "explanation" similar to first or second derivative?

share|cite|improve this question
@FlybyNight I know that, my point, I think, is that it is possible to interpret derivative in this way. Whether or not it makes sense to do so in the bigger picture, is a different question. – Valtteri Feb 6 '13 at 21:33
@FlybyNight sorry about that, was on a cruise. The wikipedia article was known to me, but thank you anyway. – Valtteri Feb 12 '13 at 18:00

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.