设方程e^(x+y) + sin(xy) = 1 确定的隐函数为y=y(x),求y'和y'|x=0
问题描述：
设方程e^(x+y) + sin(xy) = 1 确定的隐函数为y=y(x),求y'和y'|x=0
答
e^(x+y) + sin(xy) = 1 e^(x+y)*(1+y')+cos(xy)(y+xy')=0y'*[e*(x+y)+xcos(xy)]=-[ycos(xy)+e^(x+y)]y'=-[ycos(xy)+e^(x+y)]/[e*(x+y)+xcos(xy)]x=0,求出 y=0,代入上式,得到y'（x=0）=-1.