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Given a function [tex]f(x_1,\ldots,x_n)[/tex], the total derivative for [itex]x_1[/itex] is:

[tex]\frac{df}{dx_1}=\frac{\partial f}{\partial x_1}+\frac{\partial f}{\partial x_2}\frac{dx_2}{dx_1}+\ldots+\frac{\partial f}{\partial x_n}\frac{dx_n}{dx_1}[/tex]

Now, if the [itex]x_i[/itex] are just variables, can we say that:

[tex]\frac{dx_i}{dx_j}=\delta_{ij}[/tex]

?...If so, then the total derivative would equal the partial derivative:

[tex]\frac{df}{dx_1}=\frac{\partial f}{\partial x_1}[/tex]

is that correct?

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# Total derivative: elementary question

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