(c) Use the chain rule to find the derivative of the function z = 2xr*y³ – ry² along the curve given by r = cos 20, y = sin 0. Give your answer in terms of 0. (d) Determine if the function f(2) = sinh iz is complex differentiable (analytic). You may wish to note the identity sinh(r + iy) = sinh a cos y + i cosh r sin y for real numbers x, y.

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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PART D

(a) Find all second partial derivatives of
f(z, y) = e" + tan(x + y³)
(b) Find and classify the critical points of the function
f(x, y) = -2x3 – 4xy+ 2y² + 2x – 2.
(c) Use the chain rule to find the derivative of the function z = 2x*y³ – ry? along
the curve given by x = cos 20, y = sin 0. Give your answer in terms of 0.
(d) Determine if the function f(2) = sinh iz is complex differentiable (analytic).
You may wish to note the identity
sinh(x + iy) = sinh x cos y +i cosh x sin y
for real numbers r, y.
Transcribed Image Text:(a) Find all second partial derivatives of f(z, y) = e" + tan(x + y³) (b) Find and classify the critical points of the function f(x, y) = -2x3 – 4xy+ 2y² + 2x – 2. (c) Use the chain rule to find the derivative of the function z = 2x*y³ – ry? along the curve given by x = cos 20, y = sin 0. Give your answer in terms of 0. (d) Determine if the function f(2) = sinh iz is complex differentiable (analytic). You may wish to note the identity sinh(x + iy) = sinh x cos y +i cosh x sin y for real numbers r, y.
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