Answer
$f'(a)=\lim \limits_{h \to 0}\frac{-2}{a^2+ah}$, which equals to $\frac{-2}{a^2}$.
$f'(5)=\frac{-2}{5^2}=\frac{-2}{25}=-0.08$
Work Step by Step
The algebraic derivative of a function can be described as:
$f'(a)=\lim \limits_{h \to 0}\frac{f(a+h)-f(a)}{h}$
Here, $f(a)=\frac{2}{a}$
By substituting, we get:
$\frac{\frac{2}{a+h}-\frac{2}{a}}{h}=\frac{\frac{2a-2(a+h)}{(a+h)a}}{h}=\frac{\frac{-2h}{a(a+h)}}{h}=\frac{-2}{a^2+ah}$
$f'(a)=\lim \limits_{h \to 0}\frac{-2}{a^2+ah}$, which equals to $\frac{-2}{a^2}$.
$f'(5)=\frac{-2}{5^2}=\frac{-2}{25}=-0.08$
