Exploring a Wild Function: Derivative + Infinite Series + Infinite Product

This visualization treats F(x) as the sum of three strange pieces: (1) a derivative of a product involving an integral, (2) an infinite oscillating series, and (3) an infinite product. The canvas shows how each part behaves as x changes and how partial sums/products approximate the full function. You can move x, control how many terms are used in the series and product, and see how the combined F(x) is built. The left panel tracks the pieces versus x, the right panel shows local behavior near the chosen x and curvature (smoothness) via a moving tangent.