Wikipedia:Reference desk/Archives/Mathematics/2020 March 4

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March 4

meaning of equation with dx

Hi there, I recently see a lot of equation which looks like this: ${\frac {\partial }{\partial x}}x+{\frac {\partial }{\partial y}}y=1$

this is the latex format i don't know to make it a formula in media wiki code.

what is the meaning of the equation, is it x multiplied by the partial derivative plus y multiplied the partial derivative is 1. or is it the sum of the partial derivative is 1?

thanks.

--Exx8 (talk) 09:57, 4 March 2020 (UTC)

@Exx8: Wikipedia supports (essentially) LaTeX, but use <math> ... </math> instead of dollar signs. (I have done this for you above.)

About your question, can you give more context (e.g., a link to a place where you saw such a thing)? It looks to me like it might be a statement about differential operators, but it's hard to be sure. --JBL (talk) 12:55, 4 March 2020 (UTC)

@Exx8: It looks like a sum of partial derivatives. However, AFAIK ${\frac {\partial }{\partial x}}x={\frac {\partial x}{\partial x}}=1$, so I suspect something is wrong with the equation, as it implies $1+1=1$. Are you sure the equation looks like you copied above? --CiaPan (talk) 13:07, 4 March 2020 (UTC)

I just wanted to understand the meaning of this symbols, I haven't taken an equation which I've tried to solve. so the meaning of this symbol is take the derivative by x or y?

${\frac {\partial }{\partial x}}x^{2}+{\frac {\partial }{\partial y}}y^{2}=1$ this for example implies, take the partial derivative of x^2 and y^2?--Exx8 (talk) 14:27, 4 March 2020 (UTC)

@Exx8: Yes, this is a symbol of a partial derivative. In general, if an expression being differentiated is a function of several variables: $f(x,y,\ldots ,z)$ then the partial derivative of f() with respect to, say, y, is calculated as a normal derivative with respect to y assuming all other arguments being constant. See Partial derivative for more thorough and more precise explanation. --CiaPan (talk) 14:37, 4 March 2020 (UTC)

@Exx8: Just out of curiosity: How did you try to solve an equation, if you do not know the meaning of symbols used in it...? --CiaPan (talk) 09:22, 11 March 2020 (UTC)

In general, ${\frac {\partial }{\partial x}}f(x,y)$ and${\frac {\partial f(x,y)}{\partial x}}$ mean precisely the same (just like${\frac {d}{dx}}f(x)$ and${\frac {df(x)}{dx}}$ for ordinary derivatives). And ${\frac {\partial ^{2}}{\partial x\partial y}}f(x,y)$ or ${\frac {\partial ^{2}f(x,y)}{\partial x\partial y}}$ means the same as ${\frac {\partial }{\partial x}}\left({\frac {\partial }{\partial y}}f(x,y)\right).$  --Lambiam 15:12, 4 March 2020 (UTC)

Partial derivative is a good article about this. Just remember that things to the right of the fraction can also go on top of the fraction (be multiplied with the numerator), in the similar fashion as it's permissible to write either of $\int {\frac {1}{x}}\,dx=\int {\frac {dx}{x}}$ although the first form is much more common with integrals. 93.142.71.71 (talk) 21:42, 4 March 2020 (UTC)