# Need help with derivative notation

• I
If I have a scalar function of a variable ##x## I can write the derivative as: ##f'(x)=\frac{df}{dx}##.

Now suppose ##x## is no longer a single variable but a vector: ## x=(x^1, x^2, ..., x^n)##. Then of course we have for the derivative ##(\frac{\partial f}{\partial x^1}, ..., \frac{\partial f}{\partial x^n})##.

But for a proof I need a compact notation like ##\frac{df}{dx}## for this multivariable case. Does such a compact notation exist? I mean, a notation without making explicit reference to components.

fresh_42
Mentor
If I have a scalar function of a variable ##x## I can write the derivative as: ##f'(x)=\frac{df}{dx}##.

Now suppose ##x## is no longer a single variable but a vector: ## x=(x^1, x^2, ..., x^n)##. Then of course we have for the derivative ##(\frac{\partial f}{\partial x^1}, ..., \frac{\partial f}{\partial x^n})##.

But for a proof I need a compact notation like ##\frac{df}{dx}## for this multivariable case. Does such a compact notation exist? I mean, a notation without making explicit reference to components.

orion
Thanks, fresh 42. I'm sorry I'm late in responding, but I forgot I wrote this question. It turns out that after I wrote this, I realized a mistake I was making in the proof and you are right, the gradient works. Thanks again.

Mark44
Mentor
If I have a scalar function of a variable ##x## I can write the derivative as: ##f'(x)=\frac{df}{dx}##.

Now suppose ##x## is no longer a single variable but a vector: ## x=(x^1, x^2, ..., x^n)##. Then of course we have for the derivative ##(\frac{\partial f}{\partial x^1}, ..., \frac{\partial f}{\partial x^n})##.
This -- ## x=(x^1, x^2, ..., x^n)## -- should probably be written as ## x=(x_1, x_2, ..., x_n)## to avoid confusion. Although I have seen a few textbooks that use superscripts as indexes, most use superscripts to denote exponents rather than indexes.

Also, this -- ##(\frac{\partial f}{\partial x^1}, ..., \frac{\partial f}{\partial x^n})## -- should be written as ##(\frac{\partial f}{\partial x_1}, ..., \frac{\partial f}{\partial x_n})## for the same reason.
orion said:
But for a proof I need a compact notation like ##\frac{df}{dx}## for this multivariable case. Does such a compact notation exist? I mean, a notation without making explicit reference to components.