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

1 Answer
Jan 28, 2018

#-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#