# Synchronizing Colors for Functions and Derivatives in Julia Plots using RecipesBase.jl

I’m working with Julia and the `Plots.jl` package to create subplots of functions and their derivatives, and I want to synchronize the colors between corresponding functions and their derivatives using `RecipesBase.jl` . Here’s what I have so far:

``````using Plots

# Define your x-values and functions
x = 0:0.1:2π
y1 = sin.(x)
y2 = cos.(x)
y3 = tan.(x)
y4 = cot.(x)

# Calculate derivatives
dy1 = cos.(x)
dy2 = -sin.(x)
dy3 = sec.(x).^2
dy4 = -csc.(x).^2

# Define a custom color palette
my_palette = palette(:default, color=:auto, marker=:auto)

# Create the first group of subplots with synchronized colors
p1 = plot(x, y1, label="sin(x)", color=my_palette)
plot!(x, y2, label="cos(x)", color=my_palette)
plot!(x, y3, label="tan(x)", color=my_palette)
plot!(x, y4, label="cot(x)", color=my_palette)

# Create the second group of subplots with synchronized colors
p2 = plot(x, dy1, label="sin'(x)", color=my_palette, linestyle=:dash)
plot!(x, dy2, label="cos'(x)", color=my_palette, linestyle=:dash)
plot!(x, dy3, label="tan'(x)", color=my_palette, linestyle=:dash)
plot!(x, dy4, label="cot'(x)", color=my_palette, linestyle=:dash)

# Combine the subplots side by side
plot(p1, p2, layout=(1, 2), legend=true)
``````

I want to achieve the same result using `RecipesBase.jl` to define a custom recipe for color synchronization. How can I implement this using `RecipesBase.jl` ?