Answer
$-4.2x^{-3.1}-\displaystyle \frac{1}{20}x^{-0.9}$
Work Step by Step
Written in exponential form,
... sum/difference rule...
$f^{\prime}(x)=\displaystyle \frac{d}{dx}[2x^{-2.1}]-\frac{d}{dx}[\frac{1}{2}x^{0.1}]$
... constant multiple ...
$=2\displaystyle \frac{d}{dx}[x^{-2.1}]-\frac{1}{2}\frac{d}{dx}[x^{0.1}]$
... power rule...
$=2(-2.1x^{-3.1})-\displaystyle \frac{1}{2}(0.1x^{-0.9})$
$=-4.2x^{-3.1}-\displaystyle \frac{1}{20}x^{-0.9}$
