设z=f(x/y)且f是可微函数,求全微分dz
问题描述:
设z=f(x/y)且f是可微函数,求全微分dz
答
记u=x/y,则z=f(u)
u'x=1/y,u'y=-x/y^2
dz=f'u'x dx+f'u u'ydy=f'(u)(dx/y-xdy/y^2)=f'(x/y)(ydx-xdy)/y^2