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I'm reading Mary Boa's "mathematical methods in the physical sciences" and I'm on a section about total differentials.

So a total differential is for f(x, y) we know to be:

[tex] df = \frac{\partial f}{\partial x}{dx} + \frac{\partial f}{\partial y}{dy} [/tex]

Now, I've attached a problem I'm confused about. It involves taking the total differential of the reduced mass equation:

[tex] \mu^{-1} = m_1^{-1} + m_2^{-2} [/tex]

In her example, she says to take the total differential of the equation and sets the left side equal to zero. I understand why it's zero (because we want the reduced mass to be unchanged so we want [itex] \partial \mu = 0 [/itex]).

But essentially, I don't know what it means to just take the differential of [itex] \mu^{-1} [/itex] because I'm accustomed to having some defined function f(x, y) or something and if I take it's differential, I just get [itex] df [/itex].

Thanks!

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# Total Differentials

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