y=(1+x^2)^arctanx 对y求导

题目

y=(1+x^2)^arctanx 对y求导

答案

y =(1+x^2)^arcatanx
lny = arctanx.ln(1+x^2)
(1/y)y' = 2xarctanx/(1+x^2) + ln(1+x^2)/(1+x^2)
y' = [2xarcanx+ln(1+x^2)]/(1+x^2) .(1+x^2)^arctanx