The derivative of f at a point is the slope of the tangent line. Watch what happens as the gap h shrinks: the secant line through (a, f(a)) and (a+h, f(a+h)) rotates toward the tangent, and its slope approaches the true derivative f'(a). For f(x) = x^2, f'(a) = 2a.
Drag h toward 0 and the secant slope closes in on the tangent slope: that limit is the definition of the derivative. This is a fixed demonstration concept (NOVA's interactive-visual modality seed); the per-misconception, per-course generated version is the frontier work that follows.