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In this module, you will learn how to find derivatives using mathematical rules.
Lessons
Lessons
Module Start & End Dates
Module Start & End Dates
Please check the syllabus for module start & end dates.
Show Your Work Problems
Show Your Work Problems
Other Information
Other Information
Please see the course syllabus for information about project requirements and due dates.
Project 1: Equivalence of Differentiation Rules
In this module, we have learned the quotient rule for differentiating a function,
Consider the equivalent form:. Differentiate this form as is and compare it with the Quotient Rule. Discuss.
Next, rewrite f(x)g(x) as a quotient and then differentiate the quotient form as is and compare it with the Product Rule. Discuss.
Project 2: Comparing Slopes (from Stewart, 1995)
Let P be a point in the first quadrant on the graph of
.Sketch the tangent to the curve at P. The tangent line will intersect the graph of f at another point, called Q. See the graph below.
Prove that the slope of the tangent line at point Q is four times the slope at point P.
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