Let and be positive integers with

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

Problem

Let

r

and

k

be positive integers with

1\le k\le r

. For

f(x)=x^{r}

, which expression correctly gives the

k

th derivative

f^{(k)}(x)

? (a)

r!\,x^{r-k}

(b)

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

(c)

r^{k}x^{r-k}

(d)

\dfrac{r!}{k!}\,x^{r-k}

Related theory

Differentiation Rules
Higher-Order Derivatives
Advanced Differentiation
Second order derivatives
Continuity and Differentiability

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