设f x 为可导函数,y=f^2(x+arctanx),求dy/dx

题目

设f x 为可导函数,y=f^2(x+arctanx),求dy/dx

答案

令u=x+arctanx, 则u'=1+1/(1+x^2)
则y=f^2(u)
dy/dx=2f(u)f'(u)u'=2f(u)f'(u)[1+1/(x+x^2)]