Suppose: w = f (s,t) s = s (x, y) and s(1, 10) = –6 t =t(x, z) and t(1, –9) = 3 Ultimately, after substituting in the lower variables, w (x, y, z) will be a function of x, y, and z. Write down the Multivariable Chain Rule (assume everything is differentiable) formula for: Wz (1, 10, –9) = fs (???, ???)* s? (???, ???)+more terms! [Use Lagrange notation (the subscripts)!] Hint: Where do we evaluate each partial derivative?
Suppose: w = f (s,t) s = s (x, y) and s(1, 10) = –6 t =t(x, z) and t(1, –9) = 3 Ultimately, after substituting in the lower variables, w (x, y, z) will be a function of x, y, and z. Write down the Multivariable Chain Rule (assume everything is differentiable) formula for: Wz (1, 10, –9) = fs (???, ???)* s? (???, ???)+more terms! [Use Lagrange notation (the subscripts)!] Hint: Where do we evaluate each partial derivative?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Suppose:
w = f (s,t)
s = s (x, y) and s(1, 10) = -6
t =t (x, z) and t(1, –9) = 3
%3D
Ultimately, after substituting in the lower variables, w (x, y, z) will be a function of r, y, and z.
Write down the Multivariable Chain Rule (assume everything is differentiable) formula for:
Wz (1, 10, –9) = fs (???, ???)* s? (???, ???)+more terms!
[Use Lagrange notation (the subscripts)!]
Hint: Where do we evaluate each partial derivative?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc8899da1-90ac-4c1c-b86a-2d17b7ef20f6%2F297d84e9-5e44-417f-9d10-604217d48826%2Fm2cx99g_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose:
w = f (s,t)
s = s (x, y) and s(1, 10) = -6
t =t (x, z) and t(1, –9) = 3
%3D
Ultimately, after substituting in the lower variables, w (x, y, z) will be a function of r, y, and z.
Write down the Multivariable Chain Rule (assume everything is differentiable) formula for:
Wz (1, 10, –9) = fs (???, ???)* s? (???, ???)+more terms!
[Use Lagrange notation (the subscripts)!]
Hint: Where do we evaluate each partial derivative?
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