Question

How do you find the derivative using the difference quotient f ( x ) = 1 / x + 2 ?

Answer 1

`-1/[x+2]^2`

Explanation:

For a quotient, `d/dx [u/v]`=`[vdu/dx-udv/dx]/v^2`.
where u and v are both functions of x. So here let u =1 and v= x+2.
So d/dx 1/ [x+2]`=[[x+2]d/dx[1]-[1]d/dx[x+2]]/[x+2]^2`.

`d/dx 1=0. d/dx x=1`

so `d/dx[1/[x+2]]`= `-1/[x+2]^2`