Derivatives
A derivative is defined as a limit: f'(x) equals the limit as h approaches 0 of [f(x+h) - f(x)] / h, which finds the instantaneous rate of change (the slope of the tangent line) at a point. For f(x) = x^2 at x = 3: [(3+h)^2 - 9] / h = (6h + h^2) / h = 6 + h, which approaches 6 as h approaches 0, so f'(3) = 6.
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