Answer:
[tex]f'(-8)=\frac{9}{64}[/tex]
Step-by-step explanation:
Given the function
[tex]f(x)=\frac{-9}{x}[/tex]
We can rewrite it as
[tex]f(x)=-9x^{-1}[/tex]
Now we can apply the power rule
[tex]f'(x)=9x^{-2}[/tex]
Now we can rewrite it
[tex]f'(x)=\frac{9}{x^{2} }[/tex]
Now we can plug in x=-8
[tex]f'(-8)=\frac{9}{(-8)^{2} }\\f'(-8)=\frac{9}{64}[/tex]
