1,z'(x)=y+2x/（x^2+y^2）；z'(y)=x+2y/（x^2+y^2）.
2.z'(x)=2cos(x+2y)(-sin(x+2y)=-sin(2x+4y)；z'(y)=4cos(x+2y)(-sin(x+2y)=-2sin(2x+4y)；
z''(xx)=-2cos(2x+4y)；z''(xy)=z''(yx)=-4cos(2x+4y)；z''(yy)=-8cos(2x+4y)..
三.应用题
1.联立x＝y^2 y＝x－2得交点为(1,-1),(4,2).积分区域为：-1《y《2,y^2《x《y+2
所以：面积S=∫ (-1,2)dy∫ (y^2,y+2)dx=∫ (-1,2) ( y+2 - y^2) dy=[y^2/2+2y-y^3/3] |(-1,2)=9/2
2.这是一阶线性微分方程.y‘-2xy＝3x的通解为：y=e^(2x)(∫ 3xe^(-2x)dx+C)
=Ce^(2x)-3/2