##dz = \frac{\partial z}{\partial x} dx + \frac{\partial z}{\partial y} dy##(adsbygoogle = window.adsbygoogle || []).push({});

I'm confused as to how the total derivative represents the total change in a function.

My own interpretation, which I know is incorrect, is that ##\frac{\partial z}{\partial x} dx## represents change in the x direction and ##\frac{\partial z}{\partial y} dy## change in the y direction, and to get the total change you would need to square both and take the square root much like finding the magnitude of a vector.

Obviously this is not the case because, as the equation shows, you simply need to add the two terms together.

So my overarching question is: Could someone please intuitively explain what the total differential represents and why it's a simple sum?

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# Total Derivative Intuition

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