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Consider the functions z = -2e" In y, x = In (u cos v), and y = u sin v. dz dz (a) Express and du 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. dz dz (b) Evaluate and du - at (u,v) = z= - 2u cos v In (u sin v) dz du Using either method, = -2 cos v In (u sin v) - 2 cos v. (Type an expression using u and v as the variables.) dz Find each partial derivative needed to use the Chain Rule to find dz -= -2 e* In y xp -= - tan v - 2 ex dy = u cos v dz %3D dy y dv dz 2u cos v Using either method, = 2u sin v In (u sin v) dv sin v - (Type an expression using u and v as the variables.) dz (b) -2.936 (Type an exact answer.) Enter your answer in the answer box and then click Check Answer.

Consider the functions z = -2e" In y, x = In (u cos v), and y = u sin v. dz dz (a) Express and du 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. dz dz (b) Evaluate and du - at (u,v) = z= - 2u cos v In (u sin v) dz du Using either method, = -2 cos v In (u sin v) - 2 cos v. (Type an expression using u and v as the variables.) dz Find each partial derivative needed to use the Chain Rule to find dz -= -2 e* In y xp -= - tan v - 2 ex dy = u cos v dz %3D dy y dv dz 2u cos v Using either method, = 2u sin v In (u sin v) dv sin v - (Type an expression using u and v as the variables.) dz (b) -2.936 (Type an exact answer.) Enter your answer in the answer box and then click Check Answer.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter14: Discrete Dynamical Systems
Section14.3: Determining Stability
Problem 15E
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Consider the functions z= - 2 e* In y, x= In (u cos v), and y = u sin v. dz and dv dz (a) Express 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 dz dz and (b) Evaluate at (u,v) = 8, du dv - 2u cos v In (u sin v) dz Using either method, du - 2 cos v In (u sin v) – 2 cos v (Type an expression using u and v as the variables.) dz Find each partial derivative needed to use the Chain Rule to find dv dz - 2 ex In y dx dx tan v dy = u cos V dv - 2 ex dz = 2u sin v In (u sin v) - dv 2u cos v Using either method, sin v (Type an expression using u and v as the variables.) (b) - 2.936 (Type an exact answer.) (*) 8,5 Enter your answer in the answer box and then click Check Answer.
Transcribed Image Text:Consider the functions z= - 2 e* In y, x= In (u cos v), and y = u sin v. dz and dv dz (a) Express 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 dz dz and (b) Evaluate at (u,v) = 8, du dv - 2u cos v In (u sin v) dz Using either method, du - 2 cos v In (u sin v) – 2 cos v (Type an expression using u and v as the variables.) dz Find each partial derivative needed to use the Chain Rule to find dv dz - 2 ex In y dx dx tan v dy = u cos V dv - 2 ex dz = 2u sin v In (u sin v) - dv 2u cos v Using either method, sin v (Type an expression using u and v as the variables.) (b) - 2.936 (Type an exact answer.) (*) 8,5 Enter your answer in the answer box and then click Check Answer.
Consider the functions z = - 2e* In y, x= In (u cos v), and y =u sin v. dz dz and dv (a) Express 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 dz (*) dz (b) Evaluate and du at (u,v) = 8, 3 dz (a) Find each partial derivative needed to use the Chain Rule to find du dz - 2 ex In y dx 1 du u - 2 ex dy = sin v dz dy y du Express z directly in terms of u and v. Z= - 2u cos v In (u sin v) dz Using either method, - 2 cos v In (u sin v) - 2 cos v. du (Type an expression using u and v as the variables.) dz Find each partial derivative needed to use the Chain Rule to find dz dx -2 e* In y dx tan v %D %3D dv Enter your answer in the answer box and then click Check Answer.
Transcribed Image Text:Consider the functions z = - 2e* In y, x= In (u cos v), and y =u sin v. dz dz and dv (a) Express 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 dz (*) dz (b) Evaluate and du at (u,v) = 8, 3 dz (a) Find each partial derivative needed to use the Chain Rule to find du dz - 2 ex In y dx 1 du u - 2 ex dy = sin v dz dy y du Express z directly in terms of u and v. Z= - 2u cos v In (u sin v) dz Using either method, - 2 cos v In (u sin v) - 2 cos v. du (Type an expression using u and v as the variables.) dz Find each partial derivative needed to use the Chain Rule to find dz dx -2 e* In y dx tan v %D %3D dv Enter your answer in the answer box and then click Check Answer.
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