Posted by superdiver on .
How do I solve this using the TERM BY TERM method?
If f(x)= (2x^2  5x  3) / (3x)
find f'(8).

calculus 
Steve,
separate the terms:
f(x) = 2x^2/(3x)  5x/(3x)  3/(3x)
now use the quotient rule 3 times:
f'(x) = 2x(x6)/(3x)^2  15/(3x)^2  3/(3x)^2
However, this is a waste of time, since
(2x^2  5x  3) = (x3)(2x+1)
so, f(x) = (2x+1)
f'(x) = 2 as long as x≠3
so, f'(8) = 2
moral: see whether a function can be simplified before delving into long calculations.