求个题 x(1+y^2)-ln(x^2+2y)=0 求y'(0)
问题描述:
求个题 x(1+y^2)-ln(x^2+2y)=0 求y'(0)
答
x(1+y^2)-ln(x^2+2y)=0因为y是关于x的方程所以对x求导得:1+y^2+2xy*y'-1/(x^2+2y)*(2x+2y')=0把x=0代入x(1+y^2)-ln(x^2+2y)=0可解得y(0)=1/2再把x=0,y(0)=1/2代入1+y^2+2xy*y'-1/(x^2+2y)*(2x+2y')=0则5/4-2y'(0)=0...