Q2 (99 points) (A) (25%) Calculate the derivative of y = tan x at x = π/4 by first finding the derivative function and second substituting x = π/4. What is =π/4, and what do you get if you first substitute the value of y when x У x = π/4 and second find the derivative of that? Which of the these two values would you use to find the corresponding tangent line? (B) (75%) Calculate, at x = 1 and y = 1, the three partial derivatives Əz/əx, Əz/ǝy, and Ə² z/əx Əy, of the function X 1 Z + Iny cos Пх exp 1+xy 1+2xy + 3x² y² + 4x³ y³ 42+ ln(1+xytan¯¹(x/y)) You must calculate the partial derivatives by hand and show your work. A computer assisted answer will be given a grade of zero.

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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Q2 (99 points)
(A) (25%) Calculate the derivative of y = tan x at x = π/4 by first
finding the derivative function and second substituting x = π/4. What is
=π/4, and what do you get if you first substitute
the value of y when x
У
x = π/4 and second find the derivative of that? Which of the these two
values would you use to find the corresponding tangent line?
(B) (75%) Calculate, at x = 1 and y = 1, the three partial derivatives
Əz/əx, Əz/ǝy, and Ə² z/əx Əy, of the function
X
1
Z
+ Iny cos
Пх exp
1+xy
1+2xy + 3x² y² + 4x³ y³
42+ ln(1+xytan¯¹(x/y))
You must calculate the partial derivatives by hand and show your work. A
computer assisted answer will be given a grade of zero.
Transcribed Image Text:Q2 (99 points) (A) (25%) Calculate the derivative of y = tan x at x = π/4 by first finding the derivative function and second substituting x = π/4. What is =π/4, and what do you get if you first substitute the value of y when x У x = π/4 and second find the derivative of that? Which of the these two values would you use to find the corresponding tangent line? (B) (75%) Calculate, at x = 1 and y = 1, the three partial derivatives Əz/əx, Əz/ǝy, and Ə² z/əx Əy, of the function X 1 Z + Iny cos Пх exp 1+xy 1+2xy + 3x² y² + 4x³ y³ 42+ ln(1+xytan¯¹(x/y)) You must calculate the partial derivatives by hand and show your work. A computer assisted answer will be given a grade of zero.
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