证明/arctan(a)-arctan(b)/

Question

证明/arctan(a)-arctan(b)/

Answer 1

|arctan(a)-arctan(b)|/|a-b|=arctan'(x) （求导,x在ab之间）这里用了拉格朗日中值定理
所以|arctan(a)-arctan(b)|/|a-b|=1/(1+x^2)