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一阶微分形式不变性是指更改求导的中间变量后全微分的结果不变
比如z = F(x,y) ; y = E(u,v) ; x = W(u,v) ;
dz = (∂z/∂x )dx + (∂z/∂y )dy = (∂z/∂u )du + (∂z/∂v )dv;
对这题来说,
dy = (∂y/∂x )dx
设 u = lnx , v = cos3x;
则 y = u/v ;
dy = (∂y/∂u )du + (∂y/∂v )dv = (1/v)du + ( - u/(v^2) )dv
= (1/cos3x)*(1/x) + (- lnx/(cos3x*cos3x))*(-sin(3x)*3)
比如z = F(x,y) ; y = E(u,v) ; x = W(u,v) ;
dz = (∂z/∂x )dx + (∂z/∂y )dy = (∂z/∂u )du + (∂z/∂v )dv;
对这题来说,
dy = (∂y/∂x )dx
设 u = lnx , v = cos3x;
则 y = u/v ;
dy = (∂y/∂u )du + (∂y/∂v )dv = (1/v)du + ( - u/(v^2) )dv
= (1/cos3x)*(1/x) + (- lnx/(cos3x*cos3x))*(-sin(3x)*3)
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