Let , where and is a positive integer. Which of the following correctly gives the th…

MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

Let f(x)=axmf(x)=a x^{m}, where a≠0a\ne0 and mm is a positive integer. Which of the following correctly gives the rrth derivative f(r)(x)f^{(r)}(x) for 0≤r≤m0\le r\le m? (a) a (m−r)!m! xm−ra\,\dfrac{(m-r)!}{m!}\,x^{m-r} (b) a mr xm−ra\,m^{r}\,x^{m-r} (c) a m!(m−r)! xm−ra\,\dfrac{m!}{(m-r)!}\,x^{m-r} (d) a (mr) xm−ra\,{m\choose r}\,x^{m-r}

Related theory

Browse the problem library