Question

find the derivative of f(x)=(3)/(x-2) at x=4

Answer 1

f(x)=3u^-1 where u=x-2

We will be happy to critique your work.

Answer 2

rewrite
f(x) = 3(x-2)^-1
then f'(x) = -3(x-2)^-2 or -3/(x-2)^2

take it from here

Answer 3

1. f(4+h)-f(4)/h
2. (3/(4+h)-2)-(3/2) all over h
3. then im lost

Answer 4

you didn't say to find the derivative by "first principles"

dy/dx = Lim[f(4+h) - f(4)]/h as h ---> 0
= lim[3/(4+h -2) - 3/2]/h as h --->0
= lim[(6 - 3h - 6)/(2(h+2)]/h as h--> 0
= lim -3h/(2(h+2))/h as h -->0
= lim -3/(2(h+2)) as h -- >0
= =3/4