Answer
0.55
Work Step by Step
$y=f(x)=35x^{-0.35}\\\\$
...Constant Multiple Rule:$\ \ \ [cf]^{\prime}(x)=cf^{\prime}(x)$
...Power Rule$:\ \ \ [x^{n}]^{\prime}=nx^{n-1 }$
$f^{\prime}(x)=35(-0.35x^{-1.35})=\displaystyle \frac{12.25}{x^{1.35}}$.
$f^{\prime}(a)$ is the rate of change of f(x) when x=a.
For a=10,
$ f^{\prime}(10)=\displaystyle \frac{12.25}{10^{1.35}}\approx 0.547187\approx$ 0.55
