Mathematics

Problem

Let

f(x)=a x^{m}

, where

a\ne0

and

m

is a positive integer. Which of the following correctly gives the

r

th derivative

f^{(r)}(x)

for

0\le r\le m

? a)

a\,\dfrac{(m-r)!}{m!}\,x^{m-r}

a\,m^{r}\,x^{m-r}

a\,\dfrac{m!}{(m-r)!}\,x^{m-r}

a\,{m\choose r}\,x^{m-r}