Original square: area x². Adding Δx to the side adds two rectangles x·Δx and a small square (Δx)².
Area A(x) = x²
ΔA = (x+Δx)² − x² = 2x·Δx + (Δx)²
For small Δx: ΔA ≈ 2x·Δx
Derivative: A'(x) = 2x
Larger x → larger "strip" 2x·Δx for the same Δx — derivative increases.