Write a chain rule formula for the following derivative. dw for w = f(x, y, z); x = g(r, s, t), y = h(r, s, t), z = k(r, s, t) at dw dw dx dw dy + at dx dt dy at O dw at aw dw + dx dw dy dz O dw at dw dx dx at dw dy dw dz dy at dz at O dw at aw dy dw dx + ax dr dw dz %3D dy ds dz at + + + II II
Write a chain rule formula for the following derivative. dw for w = f(x, y, z); x = g(r, s, t), y = h(r, s, t), z = k(r, s, t) at dw dw dx dw dy + at dx dt dy at O dw at aw dw + dx dw dy dz O dw at dw dx dx at dw dy dw dz dy at dz at O dw at aw dy dw dx + ax dr dw dz %3D dy ds dz at + + + II II
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 91E
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Question
![Write a chain rule formula for the following derivative.
dw
for w = f(x, y, z); x = g(r, s, t), y = h(r, s, t), z = k(r, s, t)
at
dw
aw dx
+
aw dy
%3D
at
ax at
dy at
O dw
at
dw
+
dx
dw
dw
%3D
dy
aw dy
dy dt
dz
O dw
at
dw dx
dx at
dw dz
+
%3D
dz at
dw dx
ax dr
dw dz
+
dw
dw
dy
dy ds
at
az at
+
+
+](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fac0f3c56-5561-4b47-8ddf-f02546f51c3e%2F4752486b-6125-4d06-8066-e8beae4ee606%2Fxbkkyhp_processed.png&w=3840&q=75)
Transcribed Image Text:Write a chain rule formula for the following derivative.
dw
for w = f(x, y, z); x = g(r, s, t), y = h(r, s, t), z = k(r, s, t)
at
dw
aw dx
+
aw dy
%3D
at
ax at
dy at
O dw
at
dw
+
dx
dw
dw
%3D
dy
aw dy
dy dt
dz
O dw
at
dw dx
dx at
dw dz
+
%3D
dz at
dw dx
ax dr
dw dz
+
dw
dw
dy
dy ds
at
az at
+
+
+
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