Question

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

Answer 1

remember the power rule

`(dy)/(dx) x^m=mx^(m-1)`
and the constant multipule rule

`(dy)/(dx) cf(x)=c (dy)/(dx) f(x)` wher c is a constant

so


`f(x)= (-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)= (11)/(x^2)`

at x=9


`f'(9)= (11)/(9^2)`

`f'(9)= (11)/(81)`