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

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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
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

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
e^(x+y) + sin(xy) = 1
e^(x+y)*(1+y')+cos(xy)(y+xy')=0
y'*[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.

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