In this section, we will consider the derivative function rather than just at a point. We also begin looking at some of the basic derivative rules.

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Presentation transcript:

In this section, we will consider the derivative function rather than just at a point. We also begin looking at some of the basic derivative rules.

Let f be any function. The derivative function of f is defined as: provided the limit exists Other notations:

Use the definition of derivative to find the derivative of the function.

Let n be any real number (not necessarily an integer). Then:

Find the derivative of each of the following functions. (a) (b) (c)

Let f be any differentiable function, let k be any constant, and let. Then:

Let f and g be any differentiable functions, and let. Then:

Find the derivative of each of the following polynomials. (a) (b) (c)

Give the equation of the tangent line to the curve at the point (1, 3).