If g(x) = (x + 2)/(2x + 1), then g '(x) =?

Question

possible solutions

-3/(2x + 1)^2

3/(2x + 1)^2

5/(2x + 1)^2

-1/(2x + 1)^2

or is it none of these?

Answer 1

*The formula for the Quotient Rule is: [BA^1 - AB^1]/(B^2)

First: find the derivative of the numerator, represented as "A"....

A = x + 2
A^1 = 1

Sec: find the derivative of the denominator, represented as "B"...

B = 2x + 1
B^1 = 2

Third: place the original terms and derivatives in the formula....

[(2x+1)(1) - (x+2)(2)]/(2x+1)^2

*Eliminate parenthesis - use distribution, multiply the outer terms with the terms in parenthesis...

[(2x)(1) + (1)(1) - (x)(2) - (2)(2)]/(2x+1)^2

[2x + 1 - 2x - 4]/(2x+1)^2

[2x - 2x + 1 - 4]/(2x+1)^2

= - 3/(2x+1)^2

Answer 2

g(x) = (x + 2)/(2x + 1) = 1/2 + (3/2) / (2x +1),

Then g'(x) = (3/2) ( -1) 2 / (2x +1)^2.

= - 3 / ( 2x +1)^2 .Answer.

Answer 3

first one.
taking the dervative:

[(2x+1)(1) - (x+2)(2)]/(2x+1)^2

[2x+1-2x-4]/(2x+1)^2

(-3)/(2x+1)^2

Answer 4

=[2x+1-2(x+2)]/(2x+1)^2
=-3/(2x+1)^2