Differentiation from first principles
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Tangent, Gradient and Rate of Change
Equations are omitted for technical reasons - download the original pdf
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.]
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Contents of
Differentiation from first principles
1 Differentiation from First Principles Prerequisites
2 Tangent, Gradient and Rate of Change
3 Differential Calculus
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