# Symbolic function differentiation

**URL:** <https://discourse.julialang.org/t/symbolic-function-differentiation/84813>\
**Category:** General Usage\
**Tags:** symbolic\
**Created:** [July 26, 2022, 11:38am UTC](https://discourse.julialang.org/t/symbolic-function-differentiation/84813 "2022-07-26T11:38:59Z")\
**Posts on this page:** 3\
**Page:** 1

<div class="post-metadata">

**Author:** ![Starpower\_Power](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/starpower_power/32/38282_2.png) [@Starpower\_Power](https://discourse.julialang.org/u/Starpower_Power)\
**Post date:** [July 26, 2022, 11:38am UTC](https://discourse.julialang.org/t/symbolic-function-differentiation/84813/1 "2022-07-26T11:38:59Z")

</div>

in python sympy we define that x is function of t: x(t)  
and diff(x,t) is xdot  
x=sym.Function(‘x’)(t)  
how to do this thing in julia  
bcz i have to write Lagrangian equation

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<div class="post-metadata">

**Author:** ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Post date:** [July 26, 2022, 1:25pm UTC](https://discourse.julialang.org/t/symbolic-function-differentiation/84813/2 "2022-07-26T13:25:53Z")

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Look at Symbolics.jl

> **[GitHub - JuliaSymbolics/Symbolics.jl: A fast and modern CAS for a fast and...](https://github.com/JuliaSymbolics/Symbolics.jl)**
>
> A fast and modern CAS for a fast and modern language. - GitHub - JuliaSymbolics/Symbolics.jl: A fast and modern CAS for a fast and modern language.

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<div class="post-metadata">

**Author:** ![j\_verzani](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/j_verzani/32/8551_2.png) [@j\_verzani](https://discourse.julialang.org/u/j_verzani)\
**Post date:** [July 27, 2022, 7:46pm UTC](https://discourse.julialang.org/t/symbolic-function-differentiation/84813/3 "2022-07-27T19:46:51Z")

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It isn’t so different in Julia:

```julia
julia> using SymPy

julia> @syms t x() 
(t, x)

julia> diff(x(t), t)
d       
──(x(t))
dt      

```

The symbolics style, should also be mirrored:

```julia
julia> ∂ = Differential(t)
Differential(t)

julia> ∂(x(t))
d       
──(x(t))
dt      

```