Answer
$-5$
Work Step by Step
We can calculate an approximate value of $f^{\prime}(a)$ by using the formula
$f^{\prime}(a)\displaystyle \approx\frac{f(a+h)-f(a)}{h}$
(Rate of change over $[a,\ a+h]$ with a small value of $h$. )
The value $h=0.0001$ works for most examples we encounter.
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Evaluate $\displaystyle \frac{f(a+h)-f(a)}{h}$ for a=$1$, h=$0.0001$
$\displaystyle \frac{f(1.0001)-f(1)}{0.0001}=\frac{\frac{1}{(1.0001)^{5}}-\frac{1}{1^{5}}}{0.0001}$
...calculator...
$\approx-4.99850034993$
$\approx -5$
