# How to use ∂ function in my code or how to compute the mixed second-order partial derivatives or first-order cross partial derivatives of the velocity field \*\*u\*\*?

**URL:** https://discourse.julialang.org/t/how-to-use-function-in-my-code-or-how-to-compute-the-mixed-second-order-partial-derivatives-or-first-order-cross-partial-derivatives-of-the-velocity-field-u/134213
**Category:** General Usage
**Tags:** question
**Created:** [November 29, 2025, 6:44am UTC](https://discourse.julialang.org/t/how-to-use-function-in-my-code-or-how-to-compute-the-mixed-second-order-partial-derivatives-or-first-order-cross-partial-derivatives-of-the-velocity-field-u/134213 "2025-11-29T06:44:38Z")
**Posts on this page:** 1
**Showing post:** 4

<div class="post-metadata">

### Author: ![gdalle](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/gdalle/32/27854_2.png) [@gdalle](https://discourse.julialang.org/u/gdalle)
#### Post date: [November 29, 2025, 7:25am UTC](https://discourse.julialang.org/t/how-to-use-function-in-my-code-or-how-to-compute-the-mixed-second-order-partial-derivatives-or-first-order-cross-partial-derivatives-of-the-velocity-field-u/134213/4 "2025-11-29T07:25:51Z")

</div>

Where do you expect the \partial function to come from? It isn’t defined anywhere in your code. Usually, these computations are performed with an [automatic differentiation](https://juliadiff.org/) library, so unless you have an explicit formula for `∂(i, j, I, u)`, you may need to pick one of these libraries in the Julia ecosystem.

Also, please try to format your posts using the correct backticks `````, so that the code is displayed properly, see [Please read: make it easier to help you](https://discourse.julialang.org/t/please-read-make-it-easier-to-help-you/14757).

---

_[View the full topic](https://discourse.julialang.org/t/how-to-use-function-in-my-code-or-how-to-compute-the-mixed-second-order-partial-derivatives-or-first-order-cross-partial-derivatives-of-the-velocity-field-u/134213)._