• Auxiliary Procedures -- do not display

Auxiliary Procedures -- do not display

>	restart; with( plots ): with( Student[Calculus1] ):

Warning, the name changecoords has been redefined

>	f1 := (x^3-5)*(x^2-1)/(x^2+1): x1 := -2: H := [2^(2-i) $ i=0..10]: NQanim := NewtonQuotient(f1, x=x1, -3..3, 'h'=H, output=animation):

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#NQanim;

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Derivatives are an application of limits. The animation illustrates the convregence of secant lines to the tangent line at a point. The slope of the tangent line is the derivative of the function at this point.

The six lessons in this unit are organized to first develop a Conceptual Understanding of the Derivative and Precise Definition of the Derivative. A collection of Differentiation Rules are stated - and proven - for algebraic and Trigonometric Functions. These rules make it possible for us to use derivatives without having to apply the definition every time. The most powerful differentiation rule --- the Chain Rule --- is considered separately. Implicit Differentiation provides a technique for finding the slope of the tangent line to a curve even when the curve is not the graph of a function.

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