Derivate of x^p

1. Oct 8, 2004

hedlund

Let y = x^p where p is a natural number. Is it true that
$$\frac{dx^n}{d^ny} = \frac{p!}{(p-n)!} \cdot x^{p-n}$$ with the restriction that we define $$(-n)! \equiv \infty$$ for n=1,2,3... I found this formula and I believe that it is true if we define $$(-n)!$$ to equal $$\infty$$.

2. Oct 8, 2004

mathman

Your answer is correct, although you wrote the derivative upside down. The definition you used for (-n)! is the standard one.