(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 the value of y when x = π/4, and what do you get if you first substitute 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 az/x, z/ǝy, and a2z/ax ay, of the function x x = + In y cos 1+xy 2 (-/-) exp 1+2xy + 3x²y²+4x³y³ 42+ ln(1+xytan ¹(x/y)) You must calculate the partial derivatives by hand and show your work. A computer

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...
Question
(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 the value of y when x = π/4, and
what do you get if you first substitute 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 az/x, z/ǝy, and
a2z/ax ay, of the function
x
x =
+ In y cos
1+xy
2
(-/-) exp
1+2xy + 3x²y²+4x³y³
42+ ln(1+xytan ¹(x/y))
You must calculate the partial derivatives by hand and show your work. A computer
Transcribed Image Text:(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 the value of y when x = π/4, and what do you get if you first substitute 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 az/x, z/ǝy, and a2z/ax ay, of the function x x = + In y cos 1+xy 2 (-/-) exp 1+2xy + 3x²y²+4x³y³ 42+ ln(1+xytan ¹(x/y)) You must calculate the partial derivatives by hand and show your work. A computer
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