Question

Find the derivative of f(x) = -11/x at x = 9

Answer 1

rememeber

`(dy)/(dx) (ax)=a ((dy)/(dx) x)` and

`(dy)/(dx) x^m=mx^(m-1)`

so

`(dy)/(dx) ((-11)/(x) )=-11( (dy)/(dx) (1)/(x))=-11 ((-11)/(x) x^(-1))`=
`-11( -1x^(-1-1))=-11(-x^(-2))=-11( (-1)/(x^2))= (11)/(x^2)`

at x=9

11/9^2=11/81
f'(9)=11/81