Why do we use ∂ in partial differentiation for multiple variables?

[Voq]

Why we write differently d in partial derivation differentiation? Is it because of several variables?

Edited by mentor -- the action of finding a derivative is called differentiation.

 

[Orodruin]

Why we write differently d in partial derivation? Is it because of several variables?

Because it is a different concept than total derivatives and using the same notation could lead to confusion.

 

[fresh_42]

Why we write differently d in partial derivation? Is it because of several variables?

If you write it with the same symbol, make sure you will always add the direction. In this case you could write ##D_{e_i}## for the partial derivatives along the ##i-##th coordinate, ##D_v## for a directional derivative, and ##D## for the total differential or Jacobi matrix. Note, that ##D## is an operator here, which has three degrees of freedom: directions ##v##, functions ##f## and evaluation points ##x_0\, : \, D_v(f)(x_0)##. In this case it's better to avoid all other notations as ##\frac{d}{dx}## or ##\nabla f## or ##\operatorname{grad} f\,,## too.

 

[Voq]

Thank you. We use small delta for partial differentiation. I am not yet on Jacobi matrix. I need to get further grasp on concepts..

 

[Mark44]

We use small delta for partial differentiation.

No, it's actually a different character, one for which I've never seen a name.

Here are upper- and lowercase deltas: ##\Delta## and ##\delta##.
Here is the character used for partial derivatives: ##\partial##
Here is the partial of f with respect to x, using Leibniz notation: ##\frac{\partial f}{\partial x}##.
Here is the unrendered LaTeX for the above: ##\frac{\partial f}{\partial x}##.

 

[Orodruin]

No, it's actually a different character, one for which I've never seen a name.

Here are upper- and lowercase deltas: ##\Delta## and ##\delta##.
Here is the character used for partial derivatives: ##\partial##
Here is the partial of f with respect to x, using Leibniz notation: ##\frac{\partial f}{\partial x}##.
Here is the unrendered LaTeX for the above: ##\frac{\partial f}{\partial x}##.

One can also mention that the lowercase delta is sometimes used for other types of derivatives. But those are probably best left out for now.

 

[Voq]

Found this on wiki.
The character ∂ is a stylized d mainly used as a mathematical symbol to denote a partial derivative such as

(read as "the partial derivative of z with respect to x").
The symbol is referred to as "del" (not to be confused with ∇, also known as "del"), "dee", "partial dee", "partial" (especially in LaTeX), "round d","curly dee", "doh", "die" or "dabba".