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In this chapter we will start looking at the next major
topic in a calculus class. We will be
looking at derivatives in this chapter (as well as the next chapter). This chapter is devoted almost exclusively to
finding derivatives. We will be looking
at one application of them in this chapter.
We will be leaving most of the applications of derivatives to the next
chapter.
Here is a listing of the topics covered in this chapter.
The Definition of the Derivative 
In
this section we will be looking at the definition of the derivative.
Interpretation of the Derivative Here we will take a quick look at some
interpretations of the derivative.
Differentiation Formulas Here we will start introducing some of the
differentiation formulas used in a calculus course.
Product and Quotient Rule In this section we will look at
differentiating products and quotients of functions.
Derivatives of Trig Functions We’ll give the derivatives of the trig
functions in this section.
Derivatives of Exponential and Logarithm Functions In this section we will get the derivatives of
the exponential and logarithm functions.
Derivatives of Inverse Trig Functions Here we will look at the derivatives of
inverse trig functions.
Derivatives of Hyperbolic Functions Here we will look at the derivatives of
hyperbolic functions.
Chain
Rule The Chain Rule is one of the more important
differentiation rules and will allow us to differentiate a wider variety of
functions. In this section we will take
a look at it.
Implicit Differentiation In this section we will be looking at implicit
differentiation. Without this we won’t
be able to work some of the applications of derivatives.
Related Rates In this section we will look at the lone
application to derivatives in this chapter.
This topic is here rather than the next chapter because it will help to
cement in our minds one of the more important concepts about derivatives and
because it requires implicit differentiation.
Higher Order Derivatives Here we will introduce the idea of higher
order derivatives.
Logarithmic
Differentiation The topic of logarithmic differentiation is
not always presented in a standard calculus course. It is presented here for those how are
interested in seeing how it is done and the types of functions on which it can
be used.