Question

求大神帮忙，急！！

(1)设y=x arctan x，求 dy
(2)y = (1+x^2)^x，求dy

Answer 1

1. y'=arctanx+x/(1+x²)
   

   dy=[arctanx+x/(1+x²)]dx

2. lny=xln(1+x²)

   两边同时对x求导，得

   y'/y=ln(1+x²)+2x²/(1+x²)

   y'=(1+x^2)^x[ln(1+x²)+2x²/(1+x²)]

   所以

   dy=(1+x^2)^x[ln(1+x²)+2x²/(1+x²)]dx