Question

Hi. I have a question about a problem. It is:
Calculate the derivative of each function directly from the definition. f(x) equals 1/(2x+1).
The answers say it is -2/(2x+1)squared. I understand everything except how to get the correct denominator. Any help would be great!

Answer 1

if you insert 1/(2x+1) into the difference quotient and simplify then you should get the correct denominator.
Also the quotient rule will work. I can't figure out how to show a quotient, but here is a link to the rule
http://en.wikipedia.org/wiki/Quotient_rule
so you will get (0 - 2)/(2x+1)^2 or -2 / (2x+1)^2

Answer 2

When I insert in the diff quotient I get 4x^2 + 4x + 1 in the denominator, and this can be factored to (2x+1)(2x+1) or (2x+1)^2