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I have a silly question, but I seem to be confused about it. Let's say I have a function of Newton's cooling law. I measured the exponential drop of the temperature of some system and now I want to make an error analysis. Do I treat this function as a two variable function of tau (time constant in exponent) and time ? If yes, according to the error analysis I need to take partial derivatives over time and tau. This results in having time as a product in df/dtau result. Shall this be a measured time of the temperature falling to the constant level ?

In equations :

## \frac{df(\tau,t)}{d\tau} = \tau e^{-\tau t} ##

## \frac{df(\tau,t)}{dt} = t e^{-\tau t }##

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# Error analysis of a function

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