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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 poly-
nomials, 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.
By measuring slopes at points on the sine curve,
we get strong visual evidence that the derivative
of the sine function is the cosine function.
DIFFERENTIATION
RULES
3
x
ƒ=y= sin x
0
x
y
y
fª(xy= )
0
π
2
m=1 m=_1
m=0
π
2
π
π