# Scalar mixed derivative using ForwardDiff

**URL:** <https://discourse.julialang.org/t/scalar-mixed-derivative-using-forwarddiff/101517>\
**Category:** General Usage\
**Created:** [July 12, 2023, 8:57am UTC](https://discourse.julialang.org/t/scalar-mixed-derivative-using-forwarddiff/101517 "2023-07-12T08:57:27Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![Vik1](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/vik1/32/35496_2.png) [@Vik1](https://discourse.julialang.org/u/Vik1)\
**Post date:** [July 12, 2023, 8:57am UTC](https://discourse.julialang.org/t/scalar-mixed-derivative-using-forwarddiff/101517/1 "2023-07-12T08:57:27Z")

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I am trying to calculate the scalar second derivative wrt two different variables.  
To calculate the second derivative wrt one variable can be implemented as follows.

```julia
f(T, v) = T^4 * v^3

T_i = 1.0
v_i = 1.0

ForwardDiff.derivative(xx -> ForwardDiff.derivative(x -> f(T_i, x), xx), v_i) # -> 6.0

# my current working version
ForwardDiff.hessian(vv -> f(vv[1], vv[2]), [T_i, v_i])[1, 2] # -> 12.0

```

Is there a way to calculate only the scalar value I require without calculating the hessian?

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<div class="post-metadata">

**Author:** ![stevengj](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/stevengj/32/71_2.png) [@stevengj](https://discourse.julialang.org/u/stevengj)\
**Post date:** [July 12, 2023, 11:48am UTC](https://discourse.julialang.org/t/scalar-mixed-derivative-using-forwarddiff/101517/2 "2023-07-12T11:48:31Z")

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> [@Vik1](#):
>
> Is there a way to calculate only the scalar value I require without calculating the hessian?

```julia
julia> ForwardDiff.derivative(T -> ForwardDiff.derivative(v -> f(T, v), v_i), T_i)
12.0

```

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<div class="post-metadata">

**Author:** ![Vik1](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/vik1/32/35496_2.png) [@Vik1](https://discourse.julialang.org/u/Vik1)\
**Post date:** [July 12, 2023, 12:04pm UTC](https://discourse.julialang.org/t/scalar-mixed-derivative-using-forwarddiff/101517/3 "2023-07-12T12:04:13Z")

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Thank you, seems very obvious now I see it 😃