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My question is concerning the process of deriving the ideal gas equation.

I have a problem where I have to find the derivative of the ideal gas equation:

$$PV = nRT$$

My issue is with handling the constants, I am quite confident with the differentiation part.

If we rearrange the equation to get:

$$P = \frac{nRT}V$$

And take the derivative of P', I am unsure how to do this:

Do I:

$P' = 1 * 1 * \frac{T'}{V'}$, because the derivatives of n and R are both 1.

Or, do you do the following:

take $n$ and $R$ out of the derivative equation giving:

$P' = n R \frac{T'}{V'}$ and then take the derivative of $T$ and $V$ and then when calculating the final numeric value multiply by the given numeric values $n$ and $R$. In this instance $n$ is equal to 1.0 moles and $R$ is the ideal gas constant.

Sorry I feel that this is an easy answer, but I'm just uncertain.

memerson
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MEcho
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    Neither of those is correct. Try looking up the quotient rule for derivatives. – memerson Apr 27 '20 at 17:11
  • Also the scalar multiplication rule (and more generally the product rule). E.g. $(2x)'=2$ but $(2')(x')=1$. To be honest, based on this I think you should review all the basics of differentiation. – Noah Schweber Apr 27 '20 at 18:13

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