求函数z=ycos(x-2y),当x=π/4,y=π,时的全微分
问题描述：
求函数z=ycos(x-2y),当x=π/4,y=π,时的全微分
答
解dz=[-ysin(x-2y)]dx+[cos(x-2y)+2ysin(x-2y)]dy∴当x=π/4,y=π时dz=[-πsin(π/4-2π)]dx+[cos(π/4-2π)+2πsin(π/4-2π)]dy=(-√2π/2)dx+(√2/2+√2π)dy=(√2/2+√2π)dy-(√2π/2)dx