(a) Find all second partial derivatives of f(x, y) = sin(x + 2y) + ey² (b) Find and classify any critical points of the function f(x, y) = −4xy + y² + 5x − 4y + 5. (c) Use the chain rule to find the derivative of the function z = x¹y³ 3xy along the curve given by x = cos 0, y = sin 20. Give your answer in terms of 0. (d) Determine if the function f(z) = cos z is complex differentiable (analytic).
(a) Find all second partial derivatives of f(x, y) = sin(x + 2y) + ey² (b) Find and classify any critical points of the function f(x, y) = −4xy + y² + 5x − 4y + 5. (c) Use the chain rule to find the derivative of the function z = x¹y³ 3xy along the curve given by x = cos 0, y = sin 20. Give your answer in terms of 0. (d) Determine if the function f(z) = cos z is complex differentiable (analytic).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:(a) Find all second partial derivatives of
f(x, y) = sin(x + 2y) + e³²
(b) Find and classify any critical points of the function
f(x, y) = −4xy + y² + 5x − 4y + 5.
(c) Use the chain rule to find the derivative of the function z = x¹y³ 3xy along
the curve given by x = cos 0, y = sin 20. Give your answer in terms of 0.
(d) Determine if the function f(z) = cos z is complex differentiable (analytic).
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