Answer
$\displaystyle \frac{ds}{dt}=-2.31x^{-2.1}-1.2x^{-0.4}$
Work Step by Step
SUMMARY (rules in differential notation):
1. The Power Rule$:\ \ \ \displaystyle \frac{d}{dx}[x^{n}]=n\cdot x^{n-1 } $
2. Sum Rule: $\displaystyle \ \ \ \frac{d}{dx}[f\pm g](x)=\frac{d}{dx}[f(x)]\pm\frac{d}{dx}[g(x)] $
3. Constant Multiple Rule:$\ \ \displaystyle \frac{d}{dx}[cf(x)]=c\cdot\frac{d}{dx}[f(x)] $
4. Constant times x:$\ \ \ \displaystyle \frac{d}{dx}(cx)=c $
5. Constant:$\displaystyle \ \ \ \ \ \frac{d}{dx}(c)=0 $
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$ \displaystyle \frac{ds}{dt}= \frac{d}{dx}[ 2.3+2.1t^{-1.1}-2t^{0.6})$ = $\ \ \ $...(2)
$=\displaystyle \frac{d}{dt}(2.3)+\frac{d}{dt}(2.1t^{-1.1})-\frac{d}{dt}(2t^{0.6})$ = $\ \ \ $...($3$)
$=2.3\displaystyle \frac{d}{dx}( x^{0})+2.1\frac{d}{dx}(x^{-1.1})-2\frac{d}{dt}(t^{0.6})$ = $\ \ \ $...($1$)
$=0+2.1(-1.1x^{-2.1})-2(0.6x^{-0.4})$
$\displaystyle \frac{ds}{dt}=-2.31x^{-2.1}-1.2x^{-0.4}$
