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Consider the functions z= - ex In y, x= In (u cos v), and y = u sin v. dz dz (a) Express and as functions of u and v both by using the Chain Rule and by expressing z directly in terms of u and v before differentiating. du dv (b) Evaluate and dz du dz dv at (u,v) = 7, (7.7). (...) (a) Find each partial derivative needed to use the Chain Rule to find du dz dx ex In y dx əz dy du dy y Express z directly in terms of u and v z = -(u cos v) • In (u sin v) dz Using either method, = cos v. In (u sin v) - cos v ди (Type an expression using u and v as the variables.) dz Find each partial derivative needed to use the Chain Rule to find Əv dz dx əz dy = = DO 2|22|9 = = sin v DO

Consider the functions z= - ex In y, x= In (u cos v), and y = u sin v. dz dz (a) Express and as functions of u and v both by using the Chain Rule and by expressing z directly in terms of u and v before differentiating. du dv (b) Evaluate and dz du dz dv at (u,v) = 7, (7.7). (...) (a) Find each partial derivative needed to use the Chain Rule to find du dz dx ex In y dx əz dy du dy y Express z directly in terms of u and v z = -(u cos v) • In (u sin v) dz Using either method, = cos v. In (u sin v) - cos v ди (Type an expression using u and v as the variables.) dz Find each partial derivative needed to use the Chain Rule to find Əv dz dx əz dy = = DO 2|22|9 = = sin v DO

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.6: Additional Trigonometric Graphs
Problem 78E
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Consider the functions z= - ex In y, x= In (u cos v), and y = u sin v. dz dz (a) Express and as functions of u and v both by using the Chain Rule and by expressing z directly in terms of u and v before differentiating. du dv (b) Evaluate and dz du dz dv at (u,v) = 7, (7.7). (...) (a) Find each partial derivative needed to use the Chain Rule to find du dz dx ex In y dx əz dy du dy y Express z directly in terms of u and v z = -(u cos v) • In (u sin v) dz Using either method, = cos v. In (u sin v) - cos v ди (Type an expression using u and v as the variables.) dz Find each partial derivative needed to use the Chain Rule to find Əv dz dx əz dy = = DO 2|22|9 = = sin v DO
Transcribed Image Text:Consider the functions z= - ex In y, x= In (u cos v), and y = u sin v. dz dz (a) Express and as functions of u and v both by using the Chain Rule and by expressing z directly in terms of u and v before differentiating. du dv (b) Evaluate and dz du dz dv at (u,v) = 7, (7.7). (...) (a) Find each partial derivative needed to use the Chain Rule to find du dz dx ex In y dx əz dy du dy y Express z directly in terms of u and v z = -(u cos v) • In (u sin v) dz Using either method, = cos v. In (u sin v) - cos v ди (Type an expression using u and v as the variables.) dz Find each partial derivative needed to use the Chain Rule to find Əv dz dx əz dy = = DO 2|22|9 = = sin v DO
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