题目

求由这个方程y=tan(x+y)
所确定的隐函数的二阶导数d^2y/dx^2 答案是-2csc^2(x+y)*cot^3(x+y)麻烦要过程

提问时间：2021-02-28

答案

y=tan(x+y)y'=[sec(x+y)]^2*(1+y')则y'=[sec(x+y)]^2/{1-[sec(x+y)]^2}=-[sec(x+y)]^2/tan(x+y)]^2=-1/[sin(x+y)]^2则y''={-1/[sin(x+y)]^2}'={-2[sin(x+y)]cos(x+y)}*（1+y')1/[sin(x+y)]^4则y''={-2[sin(x+y)]cos(...