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

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.
Respond to this Question
Similar Questions

Maths
The 3rd term of an AP is 10 more than the first term while the fifth term is 15 more than the second term.find the sum of the 8th and 15 term of AP.if the 7th term is seven times the first term. 
calculus
How do I solve this using the TERM BY TERM method? 
math
The third term of a geometric progressiom is nine times the first term.if the second term is onetwenty fourth the fifth term.find the fourth term.ar^2=9a. r=sqr of 9 r=3.pls teach me how to get the first term and i can get the 4th … 
math
The 3rd term of a geometric progression is nine times the first term.if the second term is onetwenty fourth the 5th term.find the 4th term. solution ar^2=9a r=sqr of 9 r=3.pls help me on how to get the first term(a) 
math
the 3rd term of a geometric progression is nine times the 1st term.if the 2nd term is onetwenty fourth the 5th term.find the 4th term.(my solution so far).ar^2=9a r=sqr of 9 r=3.help me find the 1st term 
Math
The sixth term of an A.P. is 5 times the first term and the eleventh term exceeds twice the fifth term by 3 . Find the 8th term ? 
maths
in an AP the third term is equal to five times the sixth term. the second term is lesser by 3 than twice the fourth term. find the term of AP 
Maths
The sixth term of GP is 16 and the third term is 2.Find the first term and common ratio. 6th term =16 3rd term=2 So ar^5=16 and ar^2=2, then divide. So r^3=8, and r^3 =2^3. Therefore r =2 and a=1/2 
Maths
The 5th term of an arithmetic progression is 3times of 2nd term and 12th term exceeds 2times of 6th term by 1. Find the 16th term 
Maths
The 5th term of an arithmetic progression is 3times of 2nd term and 12th term exceeds 2times of 6th term by 1. Find the 16th term