🎓 Deeper Dive — Adults

Calculus has two pillars: differentiation (rate of change) and integration (accumulation/area).

Power rule: d/dx(xⁿ) = nxⁿ⁻¹. So d/dx(x³) = 3x². Integrate by reversing: ∫xⁿdx = xⁿ⁺¹/(n+1) + C.

Fundamental theorem of calculus: integration and differentiation are inverse operations. ∫ₐᵇ f'(x)dx = f(b) − f(a).

Used everywhere: physics (Newton's laws are differential equations), economics (marginal everything), AI (gradient descent).