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Partial derivatives and total differentials show your steps

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Reference no: EM13586489

Question 1: Partial Derivatives and Total Differentials (Show your steps!)

For f (x; y) = ln(x2 + y), solve for its gradient vector and Hessian matrix.

Question 2: Chain Rule (Show your steps!)

For f (x, y, z) = ln(u + z), u = x2y + zy, solve for its total di§erential. You MUST use chain rule to solve for the partial di§erentials. (Note that u is not an argument of f (.) while z is.)

Question 3: The Implicit Function Theorem (Show your steps!)

Let z = f (x, y) defined implicitly by the equation ezy = xyz. Compute ∂z/∂x and ∂z/∂y :

Question 4. Homogenous Function (Show your steps!)

Is f (x, y, z) = x2y2z2 a homogenous function or not? If so, solve for its degree. If not, prove it by showing the Eulerís Theorem is not satisfied.

Reference no: EM13586489

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