设函数y=f(x)由方程e的x次方-y的平方=xy确定,求y’和dy.
问题描述:
设函数y=f(x)由方程e的x次方-y的平方=xy确定,求y’和dy.
答
y是x的函数,对x求导则e^(x²)*(x²)'-2y*y'=x'*y+x*y'2xe^(x²)-2y*y'=y+x*y'y'=[2xe^(x²)-y]/(x+2y)dy/dx=[2xe^(x²)-y]/(x+2y)所以dy={[2xe^(x²)-y]/(x+2y)}dx