# Chain rule in Symbolics.jl
**URL:** https://discourse.julialang.org/t/chain-rule-in-symbolics-jl/63146
**Category:** Modelling & Simulations
**Tags:** symbolic
**Created:** [June 18, 2021, 4:13pm UTC](https://discourse.julialang.org/t/chain-rule-in-symbolics-jl/63146 "2021-06-18T16:13:18Z")
**Posts on this page:** 6
**Page:** 1
### Author:  [@SteffenPL](https://discourse.julialang.org/u/SteffenPL)
#### Post date: [June 18, 2021, 4:13pm UTC](https://discourse.julialang.org/t/chain-rule-in-symbolics-jl/63146/1 "2021-06-18T16:13:18Z")
Probably I’m blind,
but is there a way to get the transformation
\frac{d}{d t} x(y(t)) = \frac{\partial x}{\partial y}(y(t)) \frac{\partial y}{\partial t}(t)
where x and y are symbolic. (I want do do a symbolic transformation on a PDE).
```julia
using Symbolics
@variables t x(..) y(..)
Dt = Differential(t)
e = Dt(x(y(t)))
expand_derivatives(e) # == Differential(t)(x(y(t)))
# is there some way to get something like
# magic( e ) == Differential(y)(x) * Differential(t)(x)
```
I understand that `x(..)` implies that `x(y)` stays unevaluated. So, the above code does what it should. But I cannot find a symbolic way to trigger the chain rule. (I’m open to use other packages)
(Maybe related: [differentiation chain rule · Issue #157 · JuliaSymbolics/Symbolics.jl · GitHub](https://github.com/JuliaSymbolics/Symbolics.jl/issues/157) )
---
### Author:  [@leonandonayre](https://discourse.julialang.org/u/leonandonayre)
#### Post date: [June 19, 2021, 8:02pm UTC](https://discourse.julialang.org/t/chain-rule-in-symbolics-jl/63146/2 "2021-06-19T20:02:28Z")
I found this in the source code of Symbolics.jl
```julia
# The recursive expand_derivatives was not able to remove
# a nested Differential. We can attempt to differentiate the
# inner expression wrt to the outer iv. And leave the
# unexpandable Differential outside.
```
I am not sure, but this could be the reason?
[Symbolics.jl/src/diff.jl](https://github.com/JuliaSymbolics/Symbolics.jl/blob/master/src/diff.jl)
Mr. @shashi wrote those lines of code, probably he could help.
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### Author:  [@SteffenPL](https://discourse.julialang.org/u/SteffenPL)
#### Post date: [June 19, 2021, 8:23pm UTC](https://discourse.julialang.org/t/chain-rule-in-symbolics-jl/63146/3 "2021-06-19T20:23:49Z")
Thanks! This seems to answer the question in the sense that it’s not there yet.
I was also thinking already about implementing a function for that tasks myself. 🙂
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### Author:  [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)
#### Post date: [June 19, 2021, 9:31pm UTC](https://discourse.julialang.org/t/chain-rule-in-symbolics-jl/63146/4 "2021-06-19T21:31:32Z")
@shashi said he was working on this example.
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### Author:  [@shashi](https://discourse.julialang.org/u/shashi)
#### Post date: [June 22, 2021, 4:47pm UTC](https://discourse.julialang.org/t/chain-rule-in-symbolics-jl/63146/5 "2021-06-22T16:47:32Z")
[Apply chain rule on symbolic functions by shashi · Pull Request #273 · JuliaSymbolics/Symbolics.jl · GitHub](https://github.com/JuliaSymbolics/Symbolics.jl/pull/273) should have this feature.
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### Author:  [@SteffenPL](https://discourse.julialang.org/u/SteffenPL)
#### Post date: [June 22, 2021, 5:05pm UTC](https://discourse.julialang.org/t/chain-rule-in-symbolics-jl/63146/6 "2021-06-22T17:05:29Z")
Amazing. Thanks a lot 🙂