Question

Find the derivative of f(x) = negative 11 divided by x at x = 9.

Answer 1

Remember the power rule
$\frac{dy}{dx} x^m=mx^{m-1}$
and the constant multipule rule
$\frac{dy}{dx} cf(x)=c \frac{dy}{dx} f(x)$ wher c is  a constant

so

$f(x)= \frac{-11}{x}$ can be rewritten as
$f(x)=-11x^{-1}$
take deritivitve ad apply constnat multipule and power rule
$f'(x)=-11(-1x^{-2})$
$f'(x)=11(x^{-2})$
$f'(x)= \frac{11}{x^2}$

at x=9

$f'(9)= \frac{11}{9^2}$
$f'(9)= \frac{11}{81}$