Derivative (examples)
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Example 1

Consider f(x) = 5:

The derivative of a constant is zero.

Example 2

Consider the graph of . Should the reader have an understanding of algebra and the Cartesian coordinate system, the reader should be able to independently determine that this line has a slope of 2 at every point. Using the above quotient (along with an understanding of the limit, secant, and tangent) one can determine the slope at (4,5):

The derivative and slope are equivalent.

Example 3

Via differentiation, one can find the slope of a curve. Consider :

For any point x, the slope of the function is .

Example 4

Consider f(x) = √x:

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