Math Problem Statement
If z=xy2 and x=e−t and y=sin(t), find the following derivative using the chain rule. Enter your answer as a function of t.
dzdt=
Solution
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Math Problem Analysis
Mathematical Concepts
Calculus
Chain Rule
Product Rule
Differentiation
Formulas
Chain rule: dz/dt = (dz/dx)(dx/dt) + (dz/dy)(dy/dt)
Product rule: d(xy)/dt = (dx/dt)y + x(dy/dt)
Theorems
Chain Rule Theorem
Product Rule Theorem
Suitable Grade Level
Undergraduate Calculus (College Level)