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85问答库 > 设y=f(x,t),而t=t(x,y)可由F(x,y,t)=0确定，求dy⼀dx.

设y=f(x,t),而t=t(x,y)可由F(x,y,t)=0确定，求dy⼀dx.

f,F都是可微函数

2025-03-16 16:44:23

推荐回答（1个）

回答1：

∂
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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