# Is There a Way to Find Symbolic Roots?

**URL:** <https://discourse.julialang.org/t/is-there-a-way-to-find-symbolic-roots/50772>\
**Category:** General Usage\
**Tags:** question, package, roots, math, symbolic\
**Created:** [November 25, 2020, 8:30pm UTC](https://discourse.julialang.org/t/is-there-a-way-to-find-symbolic-roots/50772 "2020-11-25T20:30:33Z")\
**Posts on this page:** 2\
**Page:** 1

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**Author:** ![brett\_knoss](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/brett_knoss/32/13050_2.png) [@brett\_knoss](https://discourse.julialang.org/u/brett_knoss)\
**Post date:** [November 25, 2020, 8:30pm UTC](https://discourse.julialang.org/t/is-there-a-way-to-find-symbolic-roots/50772/1 "2020-11-25T20:30:33Z")

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I’m able to find a floating point approximation of the a second derivative, but I know the actual answer is log(a). Is there a way to find this symbolically?

```julia
using ModelingToolkit
using Roots 
p(t,a)=1/(1+a*exp((-t))) # let k=1
let ex = Differential(t)(p(t,a))
           func_ex = build_function(expand_derivatives(ex), t, a)
           @eval ∂tk(t,a) = ($func_ex)(t, a)
       end

let ex = Differential(t)(∂tk(t,a))
           func_ex = build_function(expand_derivatives(ex), t, a)
           @eval ∂∂tk(t,a) = ($func_ex)(t, a)      
       end 
find_zeros(∂∂tk,0,10) 

```

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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:** [November 25, 2020, 10:38pm UTC](https://discourse.julialang.org/t/is-there-a-way-to-find-symbolic-roots/50772/2 "2020-11-25T22:38:33Z")

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I think @shashi created some AbstractAlgebra integration to handle this, but I’m not certain about the state of it.