Math Problem Statement
Find the value of ∂z/∂t when (t,s)=(1,2) and z=x^4y^2−y^4x^3, x=s+t, y=s/t
Solution
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Math Problem Analysis
Mathematical Concepts
Multivariable Calculus
Partial Derivatives
Product Rule
Chain Rule
Formulas
z = x^4 y^2 - y^4 x^3
x = s + t
y = s / t
∂z/∂t = (d/dt)[(s+t)^4 * (s/t)^2] - (d/dt)[(s/t)^4 * (s+t)^3]
Theorems
Product Rule
Chain Rule
Suitable Grade Level
Grade 12 or University Level
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