# Derivative operator

**URL:** <https://community.freefem.org/t/derivative-operator/675>\
**Category:** General Discussion\
**Created:** [December 6, 2020, 11:58pm UTC](https://community.freefem.org/t/derivative-operator/675 "2020-12-06T23:58:37Z")\
**Posts on this page:** 5\
**Page:** 1

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**Author:** ![mordechaiy](https://avatars.discourse-cdn.com/v4/letter/m/cc9497/32.png) [@mordechaiy](https://community.freefem.org/u/mordechaiy)\
**Post date:** [December 6, 2020, 11:58pm UTC](https://community.freefem.org/t/derivative-operator/675/1 "2020-12-06T23:58:37Z")

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Dear FreeFem users,

I would like to ask please,  
suppose u is a “fespace” function defined on a two dimensional mesh,  
how does the operator dx(u) approximate u?

Thanks in advance,  
Mordechai.

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**Author:** ![julienG](https://yyz2.discourse-cdn.com/flex030/user_avatar/community.freefem.org/julieng/32/222_2.png) [@julienG](https://community.freefem.org/u/julienG)\
**Post date:** [December 7, 2020, 7:29am UTC](https://community.freefem.org/t/derivative-operator/675/2 "2020-12-07T07:29:33Z")

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I suggest you to read the documentation [here](https://doc.freefem.org/documentation/finite-element.html#)

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**Author:** ![mordechaiy](https://avatars.discourse-cdn.com/v4/letter/m/cc9497/32.png) [@mordechaiy](https://community.freefem.org/u/mordechaiy)\
**Post date:** [December 7, 2020, 12:22pm UTC](https://community.freefem.org/t/derivative-operator/675/3 "2020-12-07T12:22:53Z")

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Thanks Julien,  
I looked in the documentation but didn’t see any references on the dx operator.

I would like to to use a second order approximation in order to approximate the space derivatives (in x and y directions) however I don’t know if the dx operator does it already.  
And if not how can I approximate the space derivative using for example the central difference scheme (u\_i+1-u\_i-1/2h) h is length in space.

Thank you for your help!

Mordechai.

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**Author:** ![frederichecht](https://yyz2.discourse-cdn.com/flex030/user_avatar/community.freefem.org/frederichecht/32/15_2.png) [@frederichecht](https://community.freefem.org/u/frederichecht)\
**Post date:** [December 9, 2020, 4:43pm UTC](https://community.freefem.org/t/derivative-operator/675/4 "2020-12-09T16:43:15Z")

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The dx;dy, dz, … operator are build in with the finite element function code.  
you have no approximation at this level, the finite element function is piecewise polynomial  
than freefem compute the exact derivative of the polynom.

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**Author:** ![mordechaiy](https://avatars.discourse-cdn.com/v4/letter/m/cc9497/32.png) [@mordechaiy](https://community.freefem.org/u/mordechaiy)\
**Post date:** [December 14, 2020, 1:24am UTC](https://community.freefem.org/t/derivative-operator/675/5 "2020-12-14T01:24:47Z")

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Thank you very much professor Hecht.