Question

use the definition of the derivative to find the first second and third derivatives of the function

Answer 1

to solve this we need to remember the rule:

$\begin{gathered} f(x)=ax \\ f^{\prime}(x)=a \end{gathered}$

and the derivative of a constant is 0, so:

$\begin{gathered} f(x)=\frac{8}{5}x-9 \\ f^{\prime}(x)=\frac{8}{5} \\ f^{\doubleprime}(x)=0 \\ f^{\doubleprime}^{\prime}(x)=0 \end{gathered}$