# Faster way of calculate two-argument ForwardDiff gradient?

**URL:** <https://discourse.julialang.org/t/faster-way-of-calculate-two-argument-forwarddiff-gradient/33948>\
**Category:** Performance\
**Tags:** question, forward\
**Created:** [January 29, 2020, 8:47pm UTC](https://discourse.julialang.org/t/faster-way-of-calculate-two-argument-forwarddiff-gradient/33948 "2020-01-29T20:47:07Z")\
**Posts on this page:** 2\
**Page:** 1

<div class="post-metadata">

**Author:** ![longemen3000](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/longemen3000/32/7298_2.png) [@longemen3000](https://discourse.julialang.org/u/longemen3000)\
**Post date:** [January 29, 2020, 8:47pm UTC](https://discourse.julialang.org/t/faster-way-of-calculate-two-argument-forwarddiff-gradient/33948/1 "2020-01-29T20:47:07Z")

</div>

i have a function` f(x1,x2)` . sometimes i need dfdx1 , sometimes i need dfdx2, those cases are easy with the existing ForwardDiff API. the problem is when i need the two properties at once. gradient is one way, calling each time dfdx1 and dxdx2 is fine too, but is there a way to calculate two derivatives at once in one function evaluation? some example code to test

```julia
function f(x1,x2) 
res = x1+x2
  for i = 1:15
    res = sin(res)+x1 - cos(x2)
  end 
  return res
end

function df_grad(f,x1,x2)
  x = [x1,x2]
  _f = x-> f(xx[1],xx[2])
  g = ForwardDiff.gradient(_f,x)
  return g[1], g[2]
end

function df_twice(f,x1,x2)
  return ForwardDiff.derivative(x->f(x,x2),x1) , ForwardDiff.derivative(x->f(x1,x),x2)
end

```

---

<div class="post-metadata">

**Author:** ![mcabbott](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/mcabbott/32/6603_2.png) [@mcabbott](https://discourse.julialang.org/u/mcabbott)\
**Post date:** [January 29, 2020, 8:57pm UTC](https://discourse.julialang.org/t/faster-way-of-calculate-two-argument-forwarddiff-gradient/33948/2 "2020-01-29T20:57:00Z")

</div>

Here’s one solution:

```julia
function grad2(f, x1::Number, x2::Number)
    y1 = ForwardDiff.Dual(x1, (true,false))
    y2 = ForwardDiff.Dual(x2, (false,true))
    f(y1, y2).partials.values
end

@btime df_twice(f, 1, 2)
@btime grad2(f, 1, 2)

```