THEOREM 15.7 Chain Rule (One Independent Variable) Let z be a differentiable function of x and y on its domain, where x and y are differ- entiable functions of t on an interval I. Then az dy dy dt dz dz dr dt ax dt dQ/dt, where Q = Vx² + y² + z?,x = sin t, y = cos t, and z = cos t

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.2: Trigonometric Equations
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Chain Rule with one independent variable Use Theorem 15.7 to find the following derivatives.

THEOREM 15.7 Chain Rule (One Independent Variable)
Let z be a differentiable function of x and y on its domain, where x and y are differ-
entiable functions of t on an interval I. Then
az dy
dy dt
dz
dz dr
dt
ax dt
Transcribed Image Text:THEOREM 15.7 Chain Rule (One Independent Variable) Let z be a differentiable function of x and y on its domain, where x and y are differ- entiable functions of t on an interval I. Then az dy dy dt dz dz dr dt ax dt
dQ/dt, where Q = Vx² + y² + z?,x = sin t, y = cos t, and
z = cos t
Transcribed Image Text:dQ/dt, where Q = Vx² + y² + z?,x = sin t, y = cos t, and z = cos t
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