## anonymous one year ago ques

1. anonymous

Is there any significance to the notation $f^n(x)$ Like nth power of f(x) or nth order derivative of f(x) with respect to x

2. SolomonZelman

What do you really mean significance to that notation?

3. SolomonZelman

You could say $$\large\color{black}{ \displaystyle \frac{{\rm d}^n}{{\rm d}x^n} }$$

4. SolomonZelman

to use $$f^{n}(x)$$ is more convinient

5. anonymous

Is there some meaning in writing $f^n(x)$?

6. SolomonZelman

especially when you do taylor series $$\large\color{black}{ \displaystyle \frac{\left.\frac{{\rm d}^n}{{\rm d}x^n} \right|^{x=a} }{n!}(x-a)^n}$$ or would you rather use $$\large\color{black}{ \displaystyle \frac{f^{n}(a) }{n!}(x-a)^n}$$

7. SolomonZelman

it is just nth derivative of f(x)

8. anonymous

ah, makes more sense, I wanted to use it for nth power of f(x) like trigonometric functions, but I guess I'll just use $[f(x)]^n$

9. SolomonZelman

yeah, you can do that

10. SolomonZelman

I am not very good at notations, but i try not to say something like $$\large\color{black}{ \displaystyle \forall~\left\{x,y\right\}\in{\bf R}}$$

11. SolomonZelman

not all people get them, so I try to stick to regulars.... in any case, we got f^n(x) nailed i guess.