Chapter 1.3, Problem 12E

Use formulas (1) and (2) and the power rule to find the derivatives of the following functions.

$f\left(x\right)=\frac{1}{\sqrt[5]{x}}$

Derivative of Linear Function

If $f(x)=mx+b$, then we have

$f\text{'}(x)=m$. $\left(1\right)$

Constant Rule

The derivative of a constant function $f\left(x\right)=b$ is zero. That is,

$f\text{'}(x)=0$. $\left(2\right)$

Power Rule

Let $r$ be any number, and let $f\left(x\right)=x^r$. Then $f\text{'}(x)=r{x}^{r-1}$.