A Wild Function: Derivative + Infinite Series + Infinite Product

This visualization shows how the complicated function F(x) is assembled from three different building blocks:

1. A smooth term from differentiating a product involving an integral (via product rule + Fundamental Theorem of Calculus).
2. An oscillatory infinite series with decaying amplitudes.
3. An infinite product that gently rescales the result.

On the graph, you can see:

• The smooth "integral-derivative" contribution.
• The oscillatory series contribution.
• The multiplicative product contribution.
• Their combination F(x) = Term1 - Term2 - Term3.

Use the sliders to move along the x-axis and to control how many terms/ factors are used to approximate the infinite sum and product. You can also toggle visibility and animation to see each component in isolation and how partial sums and products converge to a stable shape.