 # Formulas

Listed below are the formula's for the gas laws, and their derivatives.  For the sake of space conservation, I will not be using the dx notation, but rather the f '(x) notation.  Also, each function will not be solved for any specific variable or rate.

## Boyle's Law:

Boyle's law is described by the two following formulas: PV = k, where k is a constant; P1V1 = P2V2.
The derivative of the first formula:  P'V + PV' = 0
The derivative of the second formula: P1'V1 + P1V1' = P2'V2 + P2V2'
With appropriate manipulation, one can arrive at a solution for a particular variable.
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## Charles' Law:

Charles' Law is described by the following equations: V/T = k (Again, k is constant) and V1/T1 = V2/T2.
The derivative of the first is: (V'T - T'V) / T2 = 0
The derivative of the second is: (V1'T1 - T1'V1) / (T1)2 = (V2'T2 - T2'V2) / (T2)2
One quick note: If you examine the first listed derivative, you will notice a variable will drop out (the T2), and this introduces error into the solutions.
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## Combined Gas Law:

The Combined Gas Law is described by the following equations: (PV) / T = k and (P1V1) / T1 = (P2V2) / T2
The derivative of the first is: ((P'V + V'P)T - T'PV) / T2 = 0
The derivative of the second is: ((P1'V1 + V1'P1)T1 - T1'P1V1) / (T1)2 = ((P2'V2 + V2'P2)T2 - T2'P2V2) / (T2)2
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Below are some general physics formulas as related to forces.  Again, I will not use the dx notation to save space.

## Position, Velocity, Acceleration

Position in relation to time is defined: d(t) = vt

The first derivative of position is: v(t) =