设y=y(x)是由方程x^2-y+1=e^y所确定的隐函数,求d^2y/dx^2|x=0.
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设y=y(x)是由方程x^2-y+1=e^y所确定的隐函数,求d^2y/dx^2|x=0.
为什么当x=0我求不出y的值!
为什么当x=0我求不出y的值!
x^2-y+1=e^y
2x-dy/dx=e^ydy/dx
dy/dx=2x/(1+e^y)
由2x-dy/dx=e^ydy/dx得
2-d^2y/dx^2=e^y(dy/dx)^2+e^yd^2y/dx^2
所以d^2y/dx^2=(2-e^y(dy/dx)^2)/(1+e^y)
=(2-2x^2e^y/(1+e^y)^2)/(1+e^y)
=(2(1+e^y)^2-2x^2e^y)/(1+e^y)^3
当x=0时1-y=e^y 此时该方程有唯一解 y=0
所以d^2y/dx^2|(x=0,y=0)=.1
2x-dy/dx=e^ydy/dx
dy/dx=2x/(1+e^y)
由2x-dy/dx=e^ydy/dx得
2-d^2y/dx^2=e^y(dy/dx)^2+e^yd^2y/dx^2
所以d^2y/dx^2=(2-e^y(dy/dx)^2)/(1+e^y)
=(2-2x^2e^y/(1+e^y)^2)/(1+e^y)
=(2(1+e^y)^2-2x^2e^y)/(1+e^y)^3
当x=0时1-y=e^y 此时该方程有唯一解 y=0
所以d^2y/dx^2|(x=0,y=0)=.1
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