设函数f(u)可微,且f'(0)=1/2,则Z=f(4x^2-y^2)在点(1,2)处的全微分dz是?
问题描述:
设函数f(u)可微,且f'(0)=1/2,则Z=f(4x^2-y^2)在点(1,2)处的全微分dz是?
答
设u=4x²-y² z=f(u) dz=f'(u)du
du=-2ydx+8xdy
dz=f'(0)(-4dx+8dy)=-2dx+4dy