Question

求z=e的根号下x的平方加y的平方次方的偏导数

求z=e的根号下x的平方加y的平方次方的偏导数

Answer 1

Z = e^√(x²+y²)...........(1)
ln Z = √(x²+y²)...........(2)
ln² Z = x²+y²................(3)
2ln Z Z'x/Z = 2x
Z'x = xZ/ln Z = x e^√(x²+y²)/√(x²+y²)..............(4)
类似地：
Z'y = yZ/ln Z = y e^√(x²+y²)/√(x²+y²)..............(5)

Answer 2

e^√(x2+y2)*[(x*dx+y*dy)/√(x2+y2)]

Answer 3

具体步骤如下：

追答