一道导数问题知道f'(x)=1/(1+x^2);求f(x)/(1+x^2)的导数要有过程,谢谢g(x)=f(x)/(1+x²)g'(x)=[f'(x)(1+x²)-2xf(x)]/(1+x²)²到这步我会，关键是下面的f(x)怎么求

Question

一道导数问题
知道f'(x)=1/(1+x^2);求f(x)/(1+x^2)的导数
要有过程,谢谢
g(x) = f(x)/(1+x²)
g'(x) = [f'(x)(1+x²)-2xf(x)]/(1+x²)²
到这步我会，关键是下面的f(x)怎么求

Answer 1

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刚做错了,不好意思.改过了.
g(x) = f(x)/(1+x²)
g'(x) = [f'(x)(1+x²)-2xf(x)]/(1+x²)²
= (1-2xf(x))/(1+x²)²
f(x) = ∫f'(x)dx = arctgx + C.
所以
g'(x) = (1-2xarctgx-2Cx)/(1+x²)²
...
好怪异的结果.总之求f(x)就是算不定积分,你再看看吧.