设y=f(x,t),而t=t(x,y)可由F(x,y,t)=0确定,求dy/dx.
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设y=f(x,t),而t=t(x,y)可由F(x,y,t)=0确定,求dy/dx.
f,F都是可微函数
f,F都是可微函数
![设y=f(x,t),而t=t(x,y)可由F(x,y,t)=0确定,求dy/dx.](/uploads/image/z/16619694-6-4.jpg?t=%E8%AE%BEy%3Df%28x%2Ct%29%2C%E8%80%8Ct%3Dt%28x%2Cy%29%E5%8F%AF%E7%94%B1F%28x%2Cy%2Ct%29%3D0%E7%A1%AE%E5%AE%9A%2C%E6%B1%82dy%2Fdx.)
∂
dy/dx= ∂f/ ∂x + (∂f/ ∂t)(∂t/∂x)
dF/dx= (∂F/∂t)(∂t/ ∂x)+ (∂F/∂y)(∂y/ ∂x) + (∂F/∂x)=0
dy/dx= ∂f/∂x +(∂f/∂t)[dF/dx-(∂F/∂y)(∂y/∂x)-(∂F/∂x)]/(∂F/∂t)
dy/dx= ∂f/ ∂x + (∂f/ ∂t)(∂t/∂x)
dF/dx= (∂F/∂t)(∂t/ ∂x)+ (∂F/∂y)(∂y/ ∂x) + (∂F/∂x)=0
dy/dx= ∂f/∂x +(∂f/∂t)[dF/dx-(∂F/∂y)(∂y/∂x)-(∂F/∂x)]/(∂F/∂t)
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