I know what normal differential is, dy/dx is the normal differential, where dy is the change in y for a infinitesimal change dx. Here obv, y is dependent of x. It just happens that dy/dx is also the slope of a curve at a point too. And I understand this enough to solve problems using it. Now I don’t understand what total differential is and why it is necessary. I am supposed to know this but I don’t. I don’t ever remember being briefed on this during my education, I didn’t get the memo. Can you guys please explain anew normal differential and total differential like I don’t know anything.
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By normal differential, I assume you mean partial differential (which is the usual alternative to a total differential).
If y only depends on x, they’re the same thing.
If y depends on x and z AND z depends on x, well, you could change x and leave z fixed = partial differential. Or you could change x (dy/dx) and add on how x also changes y via other stuff, ie z (dy/dz • dz/dx) = total differential.
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