# Take a derivative with respect to an expression in Symbolics

**URL:** https://discourse.julialang.org/t/take-a-derivative-with-respect-to-an-expression-in-symbolics/89900
**Category:** General Usage
**Created:** [November 7, 2022, 6:05pm UTC](https://discourse.julialang.org/t/take-a-derivative-with-respect-to-an-expression-in-symbolics/89900 "2022-11-07T18:05:27Z")
**Posts on this page:** 1
**Page:** 1

<div class="post-metadata">

### Author: ![brianguenter](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/brianguenter/32/29519_2.png) [@brianguenter](https://discourse.julialang.org/u/brianguenter)
#### Post date: [November 7, 2022, 6:05pm UTC](https://discourse.julialang.org/t/take-a-derivative-with-respect-to-an-expression-in-symbolics/89900/1 "2022-11-07T18:05:27Z")

</div>

The Symbolics documentation says (bold italic emphasis added)

```julia
struct Differential <: Symbolics.Operator

```

Represents a differential operator.

**Fields**

- `x`

: The variable or _ **expression** _ to differentiate with respect to.

This implies that one can take a derivative wrt an expression rather than a variable, although the documentation does not show such an example.

For a simple expression this works as expected:

> **Derivative wrt a simple expression rather than a variable**
>
> ```julia
> julia> using Symbolics
> 
> julia> @variables x
> 1-element Vector{Num}:
> x
> 
> julia> a = cos(x)
> cos(x)
> 
> julia> b = cos(x)
> cos(x)
> 
> julia> f = x*a
> x*cos(x)
> 
> julia> a === b
> false
> 
> julia> Da = Differential(a)
> (::Differential) (generic function with 2 methods)
> 
> julia> Db = Differential(b)
> (::Differential) (generic function with 2 methods)
> 
> julia> expand_derivatives(Da(f))
> x
> 
> julia> expand_derivatives(Db(f))
> x
> 
> ```

For a more complicated expression it doesn’t work as expected:

> **Derivative wrt a more complex expression**
>
> ```julia
> julia> a1 = cos(x)sin(x)
> cos(x)*sin(x)
> 
> julia> b1 = cos(x)sin(x)
> cos(x)*sin(x)
> 
> julia> a1 === b1
> false
> 
> julia> a1 == b1
> (cos(x)*sin(x)) == (cos(x)*sin(x))
> 
> julia> f1 = x*a1
> x*cos(x)*sin(x)
> 
> julia> Da1 = Differential(a1)
> (::Differential) (generic function with 2 methods)
> 
> julia> Db1 = Differential(b1)
> (::Differential) (generic function with 2 methods)
> 
> julia> expand_derivatives(Da1(f1))
> 0
> 
> julia> expand_derivatives(Db1(f1))
> 0
> 
> ```

Can you only take derivatives wrt simple expressions f(x) where f is one of the math functions defined in Base, and x is a variable? Or are you not supposed to take derivatives wrt expressions at all?