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
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
+
+
+
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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