Question

求第四题的二阶偏导数

Answer 1

方法如下图所示，请作参考，祝学习愉快：

Answer 2

详情如图所示

有任何疑惑，欢迎追问

Answer 3

z=∫(2->xy) cost/t dt

∂z/∂x = [cos(xy)/(xy)] y = cos(xy)/x
∂z/∂y = [cos(xy)/(xy)] x = cos(xy)/y
∂^2z/∂x^2
=∂/∂x (∂z/∂x)
=[ -x.sin(xy).y -cos(xy)] /x^2
=[ -xy.sin(xy) -cos(xy)] /x^2
∂^2z/∂y^2
=∂/∂y (∂z/∂y)
=[-y.sin(xy).x -cos(xy)]/y^2
=[-xy.sin(xy) -cos(xy)]/y^2
∂^2z/∂x∂y
=∂/∂x (∂z/∂y)
= -y.sin(xy)/y
=-sin(xy)
∂^2z/∂y∂x
=∂/∂y (∂z/∂x)
= -xsin(xy)/x
=-sin(xy)