Propagation of Uncertainty Example

Propagation of Uncertainty Examples: 1. 𝑓 (𝑥, 𝑦, 𝑧) = 𝑥 𝑦 𝑧 ! ! 𝜕𝑓 ! 𝜕𝑓 𝜕𝑓 𝛿𝑓 = +, . (𝛿𝑥 )! + , . (𝛿𝑦)! + , . (𝛿𝑧)! 𝜕𝑥 𝜕𝑦 𝜕𝑧 𝛿𝑓 = 0(𝑦𝑧)! (𝛿𝑥 )! + (𝑥𝑧)! (𝛿𝑦)! + (𝑥𝑦)! (𝛿𝑧)! ! ! 𝑓 ! 𝑓 𝑓 𝛿𝑓 = +, . (𝛿𝑥)! + , . (𝛿𝑦)! + , . (𝛿𝑧)! 𝑥 𝑦 𝑧 𝛿𝑥 ! 𝛿𝑦 ! 𝛿𝑧 ! 𝛿𝑓 = 𝑓 +, . + , . + , . 𝑥 𝑦 𝑧