# Normal derivative

**URL:** https://community.freefem.org/t/normal-derivative/1463
**Category:** General Discussion
**Created:** [January 31, 2022, 7:04pm UTC](https://community.freefem.org/t/normal-derivative/1463 "2022-01-31T19:04:24Z")
**Posts on this page:** 2
**Page:** 1

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### Author: ![zese](https://yyz2.discourse-cdn.com/flex030/user_avatar/community.freefem.org/zese/32/917_2.png) [@zese](https://community.freefem.org/u/zese)
#### Post date: [January 31, 2022, 7:04pm UTC](https://community.freefem.org/t/normal-derivative/1463/1 "2022-01-31T19:04:24Z")

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Dear all

I have two problems. first about the normal derivative. if I have a vector, u=(ux,uy) whose normal derivative is defined as du/dn. is it as : du/dn=( (dux/dx)N.x+(dux/dy)N.y , (duy/dx)N.x+(duy/dy)N.y )?  
or on the other hand, du/dn=(dux/dn, duy/dn)?  
2- to find (du/dn).n=(dux/dn N.x+ duy/dn N.y)?

BR

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<div class="post-metadata">

### 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: [February 1, 2022, 10:56am UTC](https://community.freefem.org/t/normal-derivative/1463/2 "2022-02-01T10:56:56Z")

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the second case is wrong:

you can define a

```auto
macro dn(v) ( [dx(v),dy(v)]'*[N.x,N.y]) //

```

and so  
du/dn = (dn(ux),dn(dy))