posted by HELP!! .
Find the derivative of f. you may simplify before differentiating
Surely you meant ...
f(x) = (x^2-7x+12)/(x^4-8x^3+13x^2+30x-72)
I checked by synthetic division if those factors are contained in the denominator, and they are, so
= 1/(x^2 - x - 6)
= (x^2 - x - 6)^-1
f '(x) = -(x^2 - x - 6)^-2 (2x-1)
= (1 - 2x)/(x^2 - x - 6)^2