remember the power rule
[tex] \frac{dy}{dx} x^m=mx^{m-1} [/tex]
and the constant multipule rule
[tex] \frac{dy}{dx} cf(x)=c \frac{dy}{dx} f(x)[/tex] wher c is a constant
so
[tex]f(x)= \frac{-11}{x}[/tex] can be rewritten as
[tex]f(x)=-11x^{-1}[/tex]
take deritivitve ad apply constnat multipule and power rule
[tex]f'(x)=-11(-1x^{-2})[/tex]
[tex]f'(x)=11(x^{-2})[/tex]
[tex]f'(x)= \frac{11}{x^2} [/tex]
at x=9
[tex]f'(9)= \frac{11}{9^2} [/tex]
[tex]f'(9)= \frac{11}{81} [/tex]
