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(a) What is the total differential of z = x2 + 2y2 - 2xy+ 2x- 4y - 8?

(b) Show that ∂2z/∂y∂x = ∂2z/∂x∂y for this function.

(c) Let z= xy- y + in x + 2. Find dz and show that it is exact.

(b) Show that ∂2z/∂y∂x = ∂2z/∂x∂y for this function.

(c) Let z= xy- y + in x + 2. Find dz and show that it is exact.

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