求由x+y=x^y所确定的隐函数y=y(x) 求dy/dx
问题描述：
求由x+y=x^y所确定的隐函数y=y(x) 求dy/dx
答
1+dy/dx=x^y * (y/x + dy/dx *lnx)
dy/dx=(1-x^y *y/x)/(x^y *lnx -1)
答
取对数
ln(x+y)=ylnx
微分
dln(x+y)=dylnx
1/(x+y)*d(x+y)=lnxdy+ydlnx
dx/(x+y)+dy/(x+y)=lnxdy+ydx/x
dy/dx=(x-xy-y²)/(x²+xy-x)