Math — Differentiation from First Principles

f'(x) = \lim_{h\to 0}\frac{f(x+h) - f(x)}{h}

\frac{d}{dx}x^2 = \lim_{h\to 0}\frac{(x+h)^2 - x^2}{h} = 2x

\text{gradient of the tangent}

\text{instantaneous rate of change}