# How to show that the partial derivatives exist [closed]

In general , how to show that the partial derivatives of a multivariable function exists without comupting it .

-

## closed as too broad by Michael Albanese, Joonas Ilmavirta, Daniel Rust, David K, MicahDec 14 at 22:02

There are either too many possible answers, or good answers would be too long for this format. Please add details to narrow the answer set or to isolate an issue that can be answered in a few paragraphs.If this question can be reworded to fit the rules in the help center, please edit the question.

That really depends on the circumstances. What else do you know about the function? –  fgp May 16 '13 at 21:36
I don't have a special situation but i am wondering how to show that a partial derivative exist , in general without need to compute it . –  user22323 May 16 '13 at 21:41
Any polynomial function will have partial derivatives, for example. But once you take a fraction of polynomials, it's no longer necessary. More generally, anything you can get by a sum or product or composition of 'nice' functions like sin and cos and polynomials would have partial derivatives. –  user64480 May 16 '13 at 21:48
Without a special situation, we can only refer to the definition of differentiability at a point, which involves the question of whether or not a limit exists, and thus in the general case, a computation. –  Jared May 16 '13 at 21:49
Sometimes, it is possible that you can form the difference quotients and show that the limit as $\epsilon \rightarrow 0$ exists, without explicitly computing said limit. –  Christopher A. Wong May 16 '13 at 22:07