Partial derivative. Equation of motion

Question

Would somebody,please, explain to me the following notation: $$\sigma_{xx}+d\sigma_{xx}=\sigma_{xx}+(\partial\sigma_{xx}/\partial x)\,dx. $$

I do not understand how $d\sigma_{xx}$ transforms to partial $(\partial\sigma_{xx}/\partial x)\,dx.$

Thank you in advance.

Sergey

For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to. — José Carlos Santos, Oct 31 '19 at 14:16
I would recommend a fair bit more context. What is $\sigma?$ Of how many variables is it a function? — Adrian Keister, Oct 31 '19 at 14:29
Sorry for being vague here. σ represents stress in the direction of x-axis. σ+dσ represents change of stress at the distance dσ. So I suppose that there is only one variable of this function (i.e. σ(x)) — , Oct 31 '19 at 14:50

score 0 · Accepted Answer · answered Oct 31 '19 at 16:14

0

If $\sigma_{xx}$ depends only on $x,$ then the equation $$\frac{\partial\sigma_{xx}}{\partial x}=\frac{\mathrm d\sigma_{xx}}{\mathrm dx}$$ is true, and what they've done is simply make a substitution of differentials.

answered Oct 31 '19 at 16:14

Allawonder

13,327

Thank you very much, sir. – Oct 31 '19 at 16:20
@SergeyDukman Glad to have been of help. – Allawonder Oct 31 '19 at 16:32

Partial derivative. Equation of motion

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