Differentiation from first principles

Choose a function, a point, and slide h towards zero.

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Questions students ask

What is the definition of the derivative?

f′(x) = lim as h → 0 of [f(x + h) − f(x)] / h.

What is the derivative of x² from first principles?

[(x + h)² − x²]/h = 2x + h, which tends to 2x.

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