Question

What is the total differential of w = z*e^(x+y) at (0, 0, 1) ?

Answer 1

\[dw = (\partial w/ \partial z) dz + (\partial w/ \partial x ) dx + (\partial w/ \partial y) dy\]

Answer 2

\[(\partial w/ \partial z)_{(0,0,1)} = e^{0+0} = 1, (\partial w/ \partial x)_{(0,0,1)} = 1. e^{0+0} = 1, (\partial w/\partial y)_{(0,0,1)} = 1. e ^{0+0} = 1\]

Answer 3

so dw= dz + dx + dy