Using the definition of the derivative, find the derivative of f(x) = 1/(x-3)^2
ok so first I am using the equation f(x+h)-f(x)/h
I start out with (1/(x-3)^2 +h)-1/(x-3)^2 all of that over h. then i get a common denominator for (1/(x-3)^2 +h). Then I realize something is definitely wrong. Please help me.
hmm well when I expanded numerator in [..] i got x^2+2xh+h^2-6x-6h+9. then i added and canceled terms i got -12x+18+2xh+h^2-6h. i factored out an h, -12x+18+h(2x+h+6). the i canceled the outer 1/h with the factored h and placed zero for all the remaining h's.