dy if 6 + sin 2y = dx 2y + 3x by using implicit differentiation. 2y + 3x Find Hence, find the equation of the tangent line to the curve 6 + sin 2y at the point (2,0).

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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do like example 7

dy
Find
+ 3x by using implicit differentiation.
if 6 + sin 2y = 2y
2y + 3x
Rence, find the equation of the tangent line to the curve 6 + sin zy
at the point ( 2,0).
dx
Transcribed Image Text:dy Find + 3x by using implicit differentiation. if 6 + sin 2y = 2y 2y + 3x Rence, find the equation of the tangent line to the curve 6 + sin zy at the point ( 2,0). dx
dy
dx
2xy
At (1,-1),
dy
dx
%3D
2.
y + 1
X- 1
y+ 1
X 1
x - 2
Example 7:
dy
for In cos X
dx
e'-Y = xy
a) Find
1 by using implicit differentiation.
b) Hence, find the slope at point (0, 1).
Solution:
In cos x -
el-y
xy
a)
- 1
dy
dx
sin x
+ el-y
dx
x2y
+ y
%3D
COS X
dy
dx
dy
2xy dx
el
y + tan x
dy
dx
y + tan x
- 2xy
1-y
e
12 +tan 0
%3D
m(0,1)
b)
%3D
Transcribed Image Text:dy dx 2xy At (1,-1), dy dx %3D 2. y + 1 X- 1 y+ 1 X 1 x - 2 Example 7: dy for In cos X dx e'-Y = xy a) Find 1 by using implicit differentiation. b) Hence, find the slope at point (0, 1). Solution: In cos x - el-y xy a) - 1 dy dx sin x + el-y dx x2y + y %3D COS X dy dx dy 2xy dx el y + tan x dy dx y + tan x - 2xy 1-y e 12 +tan 0 %3D m(0,1) b) %3D
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