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Is there such a thing in math as the rate of change of time with respect to another variable?
I know that you can use differential calculus to find the rates of change of several variables such as velocity or distance. But I'm trying to talk about how the time it takes for a program to run changes with the size of the data. So is there such a thing as the rate of change of time with respect to data size (or any variable?)
2 Answers
- ThomasLv 76 years ago
Well yes. Suppose you have a function t(d) where t is dependent on the amount of data. Furthermore, suppose there is a function d(x) where the amount of data depends on a variable x
You can take the derivatives of both...
dt/dd and dd/dx then dx/dt would be equal to
dx/dt=(dx/dt)(dt/dd)
- Jeff AaronLv 76 years ago
Yes. It would be the reciprocal of the rate of change of that other variable (e.g. data size) with respect to time.
dt/dd = 1 / (dd/dt)
For example, if your speed is 50 mph, the rate of change of distance with respect to time is 50 (miles per hour), so the rate of change of time with respect to distance is 0.2 (hours per mile).
