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Differentiation from first principles


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Tangent, Gradient and Rate of Change


A tangent is a line just touching a curve. Provided the curve has no sharp points there is just one tangent at every point. [Diagram goes here - download the original pdf to see it.] The gradient of the tangent at a of a function f(x) represents the instantaneous rate of change of that function at a. [Diagram goes here - download the original pdf to see it.] As the diagram indicates, the gradient can be found by graphical means. [Equation goes here - download the original pdf to see it.]
Contents of
Differentiation from first principles

1 Differentiation from First Principles Prerequisites
2 Tangent, Gradient and Rate of Change
3 Differential Calculus

Related articles: (1) Calculus:summary, (2) Limiting processes