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Calculus I - Notes

Internet Explorer 10 & 11 Users : If you have been using Internet Explorer 10 or 11 to view the site (or did at one point anyway) then you know that the equations were not properly placed on the pages unless you put IE into "Compatibility Mode". I believe that I have partially figured out a way around that and have implimented the "fix" in the Algebra notes (not the practice/assignment problems yet). It's not perfect as some equations that are "inline" (i.e. equations that are in sentences as opposed to those on lines by themselves) are now shifted upwards or downwards slightly but it is better than it was.

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 Limits Previous Chapter Next Chapter Applications of Derivatives The Definition of the Limit Previous Section Next Section The Definition of the Derivative

## Derivatives

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 who are interested in seeing how it is done and the types of functions on which it can be used.

 The Definition of the Limit Previous Section Next Section The Definition of the Derivative Limits Previous Chapter Next Chapter Applications of Derivatives

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