# \[ReverseDiff.jl\] How to do nested differentiation?

**URL:** <https://discourse.julialang.org/t/reversediff-jl-how-to-do-nested-differentiation/95542>\
**Category:** Machine Learning\
**Created:** [March 4, 2023, 2:00pm UTC](https://discourse.julialang.org/t/reversediff-jl-how-to-do-nested-differentiation/95542 "2023-03-04T14:00:11Z")\
**Posts on this page:** 1\
**Page:** 1

<div class="post-metadata">

**Author:** ![mariusd](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/mariusd/32/23231_2.png) [@mariusd](https://discourse.julialang.org/u/mariusd)\
**Post date:** [March 4, 2023, 2:00pm UTC](https://discourse.julialang.org/t/reversediff-jl-how-to-do-nested-differentiation/95542/1 "2023-03-04T14:00:12Z")

</div>

See the following example. I do calculate the derivative of `f` w.r.t. to `x`, called `fx`. Then I calculate the derivative of `fx` w.r.t. to `y`, called `fxy`. The function `fxyz` is computed similarly.  
The output of `fx` is correct, but `fxy` and `fxyz` give incorrect results. What is the proper way to do this with ReverseDiff?

```julia
using ReverseDiff: gradient

# the function of interest
f(x, y, z) = x.*y.*z

fx(x, y, z) = gradient(x->f(x, y, z), x)
fxy(x, y, z) = gradient(y->fx(x, y, z), y)
fxyz(x, y, z) = gradient(z->fxy(x, y, z), z)

inputs = ([1.f0], [2.f0], [3.f0])
fx(inputs...) # output is [6.f0], CORRECT
fxy(inputs...) # output is [0.f0], WRONG, shall be [3.f0]
fxyz(inputs...) # output is [0.f0], WRONG, shall be [1.f0]

```