Question

Is this the correct notation?

Answer 1

Given some power function:
\(f(x)=x^{n}\)

Its \(k\)'th derivative is:
\(\color{blue}{f^{k}(x) =\left(\begin{matrix}n-k \\ n\end{matrix}\right)x^{n-k}}\)

Answer 2

Nice presentation of the formula. However, you haven't included any instructions. What's the purpose of your post?

Answer 3

Can you describe in words the purpose of this formula?

Answer 4

I think your k derivative is kinda messed up
for example n-k is less than n

Answer 5

let's look at an example:
\[f(x)=x^4 \\ f^{(1)}(x)=4x^3 \\ f^{(2)}(x)=4(3)x^{2} \\ f^{(3)}(x)=4(3)(2)x^1 \\ f^{(4)}(x)=4(3)(2)(1)x^{0} \\\]
try to find a pattern here
if you can't find it let me know and maybe I can give another hint
like just first try to find a general formula for the first 4 derivatives of x^4