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Use implicit differentiation to find the gradient of the tangent line for xy 6xy - 2x = 9 at the point (-1,1).

Use implicit differentiation to find the gradient of the tangent line for xy 6xy - 2x = 9 at the point (-1,1).

Calculus: Early Transcendentals
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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26. do no 5 only , do like example 5 given

Use implicit differentiation to find the gradient of the tangent to the curve nd the equation of the tangent line to the curve ind the equation of the tangent line to the curve x xy + 3y = 26 TANGENT LINE AND IMPLICIT DIFFERENTIATION Find the equation of the tangent line to the curve xy = 4 + In x at the point (1 MAT 42 TUTORIAL 26 6 at Q(-1,2). 2. * * xy - y = 1 at the point (2, 3). 3. sin xy = y at (, 1). at the gradient of the tangent to the curve v (x + 2) + tan 2x - 8 = 0 the point (0,2). Use implicit differentiation to find the gradient of the tangent line for x'y 6xy - 2x = 9 at the point (-1, 1). Use implicit differentiation to find the gradient of the tangent line for + 2 sin x = 4y at the point (n, 2). y dy dx Hence, find the equation of the tangent line to the curve 6 + sin 2y : Find if 6 + sin 2y = 2y° + 3x by using implicit differentiation. 2y + 3x %3D at the point (2,0). lee implicit differentiation to find the equation of the tangent line to the curve + sin x = 2y at the point (t, 2). the point ( 1, 2). at f the tangent
Transcribed Image Text:Use implicit differentiation to find the gradient of the tangent to the curve nd the equation of the tangent line to the curve ind the equation of the tangent line to the curve x xy + 3y = 26 TANGENT LINE AND IMPLICIT DIFFERENTIATION Find the equation of the tangent line to the curve xy = 4 + In x at the point (1 MAT 42 TUTORIAL 26 6 at Q(-1,2). 2. * * xy - y = 1 at the point (2, 3). 3. sin xy = y at (, 1). at the gradient of the tangent to the curve v (x + 2) + tan 2x - 8 = 0 the point (0,2). Use implicit differentiation to find the gradient of the tangent line for x'y 6xy - 2x = 9 at the point (-1, 1). Use implicit differentiation to find the gradient of the tangent line for + 2 sin x = 4y at the point (n, 2). y dy dx Hence, find the equation of the tangent line to the curve 6 + sin 2y : Find if 6 + sin 2y = 2y° + 3x by using implicit differentiation. 2y + 3x %3D at the point (2,0). lee implicit differentiation to find the equation of the tangent line to the curve + sin x = 2y at the point (t, 2). the point ( 1, 2). at f the tangent
+ COS At (7, 2); 3 (2) dx dy dy 12 dx 1 = dy 8 dx 1. 1 dy dx %3D 8. Example 5: Use implicit differentiation to find the equation of the tangent line to the curve e - 2x = (y - 1) + 4 cos y at y = 0. Solution: - 2x (y - 1)° + 4 cos y exy %3D (-1)° + 4 cos 0 - 1 + 4 - 2 - 1 At y = 0, e° 2x %3D 1 - 2x %3D 2x %3D %3D dy 5 (y - 1) - 4 sin y dy dx e"(x + y) - 2 At (-1,0) + 0) e(-dx dy 5(-1)*dy - 2 dy - 2 dx dy dx %3D dy dx 1 3 y - 0 X + 1 %3D y %3D 1/3 1/3113 11
Transcribed Image Text:+ COS At (7, 2); 3 (2) dx dy dy 12 dx 1 = dy 8 dx 1. 1 dy dx %3D 8. Example 5: Use implicit differentiation to find the equation of the tangent line to the curve e - 2x = (y - 1) + 4 cos y at y = 0. Solution: - 2x (y - 1)° + 4 cos y exy %3D (-1)° + 4 cos 0 - 1 + 4 - 2 - 1 At y = 0, e° 2x %3D 1 - 2x %3D 2x %3D %3D dy 5 (y - 1) - 4 sin y dy dx e"(x + y) - 2 At (-1,0) + 0) e(-dx dy 5(-1)*dy - 2 dy - 2 dx dy dx %3D dy dx 1 3 y - 0 X + 1 %3D y %3D 1/3 1/3113 11
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