The significance of partial derivative notationIf some function like f depends on just one variable...

lascieflYr

lascieflYr

Answered

2022-11-30

The significance of partial derivative notation
If some function like f depends on just one variable like x, we denote its derivative with respect to the variable by:
d d x f ( x )
Now if the function happens to depend on n variables we denote its derivative with respect to the ith variable by:
x i f ( x 1 , , x i , , x n )
Now my question is what is the significance of this notation? I mean what will be wrong if we show "Partial derivative" of f with respect to x i like this? :
d d x i f ( x 1 , , x i , , x n )
Does the symbol have a significant meaning?

Answer & Explanation

moralizoL31

moralizoL31

Expert

2022-12-01Added 9 answers

Or from a mathematical standpoint:
d d x i f ( x 1 , , x i , , x n ) = j = 1 n x j f ( x 1 , , x n ) · d x j d x i
that is, the partial derivative "binds closer" to f than the total derivative.

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