f（x）=ax+1/(x+b)
f'(x)=(ax)' + (1/(x+b))'
=a - (x+b)'/(x+b)^2
= a - 1/(x+b)^2
另：如果题目是f（x）=(ax+1)/(x+b)
f‘(x) = [ (x+b)*(ax+1)' - (ax+1) * (x+b)' ] / (x+b)^2
= [ (x+b)*a - (ax+1) * 1 ] / (x+b)^2
= [ ax+ab- ax-1 ] / (x+b)^2
=(ab-1) / (x+b)^2