设z=ln(eu+v),v=xy,u=x2-y2,求dz/dx,dz/dy.
问题描述:
设z=ln(eu+v),v=xy,u=x2-y2,求dz/dx,dz/dy.
答
说明:eu应该是e的x次幂,dz/dx,dz/dy应该是偏导数.
∵v=xy,u=x2-y2
∴du/dx=2x,du/dy=-2y,dv/dx=y,dv/dy=x
∵z=ln(e^u+v),
∴dz/dx=[(e^u)/(e^u+v)](du/dx)+[1/(e^u+v)](dv/dx)
=(2xe^u+y)/(e^u+v)
dz/dy=[e^u/(e^u+v)](du/dy)+[1/(e^u+v)](dv/dy)
=(-2ye^u+x)/(e^u+v).