A What Is The Total Differential

(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.

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