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The graph of the function w = f(x, y) is shown below. (a) Assume that x and y are functions of a single variable r. Give the chain rule for finding dw/dr. dw aw dx aw dy + dr ax dr ay dr dw dr dw dr O dw dr dw dr aw ar dw dr aw ar aw ar aw 80 aw 80 aw 80 = aw 80 = aw 80 = (b) Assume that x and y are functions of two variables rand 8. Give the chain rule for finding aw/ar. aw aw ax aw ay ar ax ar ay ər = = = = dw ax + aw dy ax dr dy ar = dw dx dx dr = aw ax ax ar dw dx dx dr dw ax ax dr dw dx dx dr aw dx dx ar aw dx ax dr dw ax dx ae dw ax ax de + aw dx dx 30 + aw ax ax ae + + Give the chain fule for finding aw/80. aw dx ax de + + + + + + + aw ay ay ar + dw dy dy dr + dw dy dy dr dw ay ay dr dw dy dy dr aw dy dy ar aw dy ay dr aw dy ay de dw ay dy ae dw ay ay de aw dy dy ae aw ay ay ae

The graph of the function w = f(x, y) is shown below. (a) Assume that x and y are functions of a single variable r. Give the chain rule for finding dw/dr. dw aw dx aw dy + dr ax dr ay dr dw dr dw dr O dw dr dw dr aw ar dw dr aw ar aw ar aw 80 aw 80 aw 80 = aw 80 = aw 80 = (b) Assume that x and y are functions of two variables rand 8. Give the chain rule for finding aw/ar. aw aw ax aw ay ar ax ar ay ər = = = = dw ax + aw dy ax dr dy ar = dw dx dx dr = aw ax ax ar dw dx dx dr dw ax ax dr dw dx dx dr aw dx dx ar aw dx ax dr dw ax dx ae dw ax ax de + aw dx dx 30 + aw ax ax ae + + Give the chain fule for finding aw/80. aw dx ax de + + + + + + + aw ay ay ar + dw dy dy dr + dw dy dy dr dw ay ay dr dw dy dy dr aw dy dy ar aw dy ay dr aw dy ay de dw ay dy ae dw ay ay de aw dy dy ae aw ay ay ae

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.3: The Natural Exponential Function
Problem 51E
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The graph of the function w = f(x, y) is shown below. (a) Assume that x and y are functions of a single variable r. Give the chain rule for finding dw/dr. aw dx aw dy ax dr ay dr dw dr dw dw dw dr dw dr aw ar dw dr aw ar aw ar aw 30 = aw 80 = aw 20 = = = = = = = dw ax ax dr (b) Assume that x and y are functions of two variables r and 8. Give the chain rule for finding aw/ər. aw aw ay aw ax + ax ar ar ay ər = dw dx dx dr = aw ax əx ər dw dx dx dr dw dx dx dr aw dx dx ar + dw ax + ax dr dw ax dx 80 + dw ax ax de + aw dx dx 80 + aw ax ax 20 + + Give the chain fule for finding aw/80. aw_aw dx = 30 ax de aw 30 + + aw dx aw dy + ax dr ay dr + aw dy dy ar + aw ay ?у аг + dw dy dy dr + dw dy dy dr dw ay ay dr dw dy dy dr aw dy dy ar aw dy ay de dw ay dy ae dw ay ay de aw dy dy 80 aw ay ay ae
Transcribed Image Text:The graph of the function w = f(x, y) is shown below. (a) Assume that x and y are functions of a single variable r. Give the chain rule for finding dw/dr. aw dx aw dy ax dr ay dr dw dr dw dw dw dr dw dr aw ar dw dr aw ar aw ar aw 30 = aw 80 = aw 20 = = = = = = = dw ax ax dr (b) Assume that x and y are functions of two variables r and 8. Give the chain rule for finding aw/ər. aw aw ay aw ax + ax ar ar ay ər = dw dx dx dr = aw ax əx ər dw dx dx dr dw dx dx dr aw dx dx ar + dw ax + ax dr dw ax dx 80 + dw ax ax de + aw dx dx 80 + aw ax ax 20 + + Give the chain fule for finding aw/80. aw_aw dx = 30 ax de aw 30 + + aw dx aw dy + ax dr ay dr + aw dy dy ar + aw ay ?у аг + dw dy dy dr + dw dy dy dr dw ay ay dr dw dy dy dr aw dy dy ar aw dy ay de dw ay dy ae dw ay ay de aw dy dy 80 aw ay ay ae
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