Math Problem Statement
Use the Chain Rule to find dz/dt . Where:
z=cos(x+8y),x=t4,y=3t
∂z/∂x=
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dx/dt=
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∂z/∂y=
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dy/dt=
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Solution
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Math Problem Analysis
Mathematical Concepts
Calculus
Chain Rule
Partial Derivatives
Trigonometric Functions
Formulas
∂z/∂x = -sin(x + 8y)
dx/dt = 4t^3
∂z/∂y = -8sin(x + 8y)
dy/dt = 3
dz/dt = ∂z/∂x * dx/dt + ∂z/∂y * dy/dt
Theorems
Chain Rule
Suitable Grade Level
Undergraduate Calculus
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