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Computer algebra systems have commands that differentiate functions, but the form of the answer may not be convenient and so further commands may be necessary to simplify the answer.(a) Use a CAS to find the derivative in Example 3 and compare with the answer in that example. Then use the simplify command and compare again.(b) Use a CAS to find the derivative in Example 6. What happens if you use the simplify command? What happens if you use the factor command? Which form of the answer would be best for locating horizontal tangents?

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a. $\frac{45(t-2)^{8}}{(2 t+1)^{10}}$b. 2$(2 x+1)^{4}\left(x^{3}-x+1\right)^{3}\left(17 x^{3}+6 x^{2}-9 x+3\right)$

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 4

The Chain Rule

Derivatives

Differentiation

Oregon State University

Harvey Mudd College

Idaho State University

Boston College

Lectures

04:40

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

44:57

In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.

11:31

Computer algebra systems h…

03:29

Use the power rule to find…

04:03

Use the product rule and t…

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