导数 f(x)=ax+1/(x+b) (a、b∈Z) 求导f(x)=ax+1/(x+b) (a、b∈Z) 求导

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导数 f(x)=ax+1/(x+b) (a、b∈Z) 求导f(x)=ax+1/(x+b) (a、b∈Z) 求导

导数 f(x)=ax+1/(x+b) (a、b∈Z) 求导f(x)=ax+1/(x+b) (a、b∈Z) 求导
导数 f(x)=ax+1/(x+b) (a、b∈Z) 求导
f(x)=ax+1/(x+b) (a、b∈Z) 求导

导数 f(x)=ax+1/(x+b) (a、b∈Z) 求导f(x)=ax+1/(x+b) (a、b∈Z) 求导
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

ab-1/(x+b)²