设函数 z=(2x+y)^x+2y 求dz

1个回答

dz=zxdx+zydy
=[(2x+y)^x+2y]'xdx+ [(2x+y)^x+2y]'ydy
={e^[xln(2x+y)]+2y}'xdx+[x(2x+y)^(x-1)+2]dy
=e^[xln(2x+y)][ln(2x+y)+(2x/2x+y)]dx+[x(2x+y)^(x-1)+2]dy
=[(2x+y)^x][ln(2x+y)+(2x/2x+y)]dx+[x·(2x+y)^(x-1)+2]dy