My name is Alexander FufaeV and here I write about:
What is the Difference Between Partial and Total Derivative?
The difference between a partial derivative \(\frac{\partial f(x,y)}{\partial x}\) to \(x\) and a total derivative \(\frac{\text{d}f(x,y)}{\text{d}x}\) to \(x\) is that in the partial derivative it is assumed that \(y\) is independent of \(x\).
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In the partial derivative \(\frac{\partial f(x,y)}{\partial x}\) \(y\) is kept constant.
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The total derivative \(\frac{\text{d}f(x,y(x))}{\text{d}x}\) does NOT assume that \(y\) is constant. The change of \(x\) also affects \(y\).