Math Problem Statement

u=XY+yz+zx,X=1/t,y=e^tz=e^-t find du/dt​

Solution

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Math Problem Analysis

Mathematical Concepts

Differentiation
Exponential Functions
Quotient Rule
Product Rule

Formulas

u = XY + yz + zx
X = 1/t, y = e^t, z = e^{-t}
du/dt = d/dt(XY) + d/dt(yz) + d/dt(zx)
Quotient Rule: d/dt(f/g) = (g f' - f g')/g^2

Theorems

Product Rule
Quotient Rule
Chain Rule

Suitable Grade Level

Undergraduate Calculus