James Stewart-Calculus_ Early Transcendentals-Cengage Learning (2015)

3
Differentiation Rules
In the project on page 208
you will calculate the distance
from an airport runway at
which a pilot should start
descent for a smooth landing.
© Mechanik / Shutterstock.com
we have seen how to interpret derivatives as slopes and rates of change. We have seen
how to estimate derivatives of functions given by tables of values. We have learned how to graph
derivatives of functions that are defined graphically. We have used the definition of a derivative to
calculate the derivatives of functions defined by formulas. But it would be tedious if we always
had to use the definition, so in this chapter we develop rules for finding derivatives without having
to use the definition directly. These differentiation rules enable us to calculate with relative
ease the derivatives of polynomials, rational functions, algebraic functions, exponential and logarithmic
functions, and trigonometric and inverse trigonometric functions. We then use these rules
to solve problems involving rates of change and the approximation of functions.
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