Question

用对数求导法求y=x^2×√x+1/x+2的导数

Answer 1

问：用对数求导法求y=x^2×√x+1/x+2的导数

答：题目有点问题，应改为y=((1/x)+x)^x的导数

答：用对数求导法：y=(x+(1/x))^x同对数：lny=x*ln(x+(1/x))同对x求导：y'/y=ln(x+(1/x))+x*(1-x^(-2))/(x+(1/x))y'/y=ln(x+(1/x))+(x-(1/x))/(x+(1/x))y'/y=ln(x+(1/x))+(x^2-1)/(x^2+1)y'=[ln(x+(1/x))+(x^2-1)/(x^2+1)]*(x+(1/x))^x