Partial derivatives of a multivariable function.

Asked Feb 09 '22 at 16:22

Active Feb 10 '22 at 02:14

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Let $f(x,y)$ be a two-variable function. Then I saw in my book that, $$ df =\frac{\partial f}{\partial x}\mathrm{dx}+\frac{\partial f}{\partial y}\mathrm{dy}$$ MY QUESTION:-

$(1)$ How to prove this?

I made several attempts but i suspect I am missing something important.

edited Feb 10 '22 at 02:14

asked Feb 09 '22 at 16:22

RAHUL

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This essentially boils down to definitions of the symbols involved; see Help understanding expression for the derivative of a function. Also, it should be $df$ not $\partial f$. – peek-a-boo Feb 09 '22 at 22:04
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Consider a parameterisation of $f$ in terms of $t$ i.e $f(x,y) = f(x(t), y(t))$. What is the total derivative $df/dt$? – Matthew Cassell Feb 10 '22 at 05:06
This might also be helpful besides the already provided link. – Dan Doe Feb 11 '22 at 15:55

Partial derivatives of a multivariable function.

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