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Product Rule Teacher Resources
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In the first example, instead of actually using the quotient rule, Sal rewrites the denominator as a negative exponent and uses the product rule. In subsequent examples, Sal shows, but does not prove, the derivative of several interesting functions including ex, ln x, sin x, cos x, and tan x.
Using a specific example, Sal shows how to find the equation of a tangent line to a given function at a specific point. Specifically, he solves the problem of finding the tangent line to the function f(x) = xex at x = 1. This problem provides a review of the product rule, slope-intercept form of a line, and steps for finding the equation of a line. It also, provides a nice visual understanding of the problem by graphing both the original equation and the found tangent line.
Twelfth graders explore the concept of limits. In this calculus lesson plan, 12th graders investigate the limit rules for both finite and infinite limits through the use of the TI-89 calculator. The worksheet includes examples for each rule and a section for students to try other examples.
In this calculus learning exercise, learners solve 10 different problems that include determining the first derivative in each. First, they apply properties of logarithmic functions to expand the right side of each equation. Then, students differentiate both sides with respect to x,using the chain rule on the left side and the product rule on the right. In addition, they multiply both sides by y and substitute.
This lesson plan provides an introduction to integration by parts. It helps learners first recognize derivatives produced by the product rule and then continues with step-by-step instructions on computing these integrals. It also shows integrating special forms with e and trigonometric functions. This resource includes handouts and a practice worksheet.
Students investigate derivatives using the product rule. In this derivatives using the product rule lesson, students use the Ti-89 to find the derivatives of functions such as x^2 and sin(x) using the product rule. Students visualize the process of finding the derivatives using the product rule on the Ti-89.
Students construct the graph of derivatives using a tangent line. For this construction of a graph of a derivative lesson, students use their Ti-Nspire to drag a tangent line along a graph. Students graph the slope of the tangent line. Students discuss the similarities and differences between the original graph and its derivative.
In this Calculus worksheet, students assess their understanding of various topics, including the derivatives of trigonometric functions, evaluating integrals, sigma notation, and convergent and divergent series. The one page interactive worksheet contains fifty-two problems. Answers are not provided.
In this Calculus instructional activity, students use a graphing calculator to boost their understanding of functions and their graphs as they examine the properties of curves. The forty-two page instructional activity contains one hundred problems. Answers are not provided.
In this exam review worksheet, students find the limits of given problems. They identify the slope of a line tangent to a function. Students find the derivative of a function. They determine the area between two curves. This four-page worksheet contains 21 multi-step problems.
Students assess transformations to remove integral symbols as well as to simplify expressions. They explore the Symbolic Math Guide to assist them in solving indefinite integration by parts. This lesson includes partial fractions, sum/difference and scalar product transformations.
This lesson looks at rational polynomial functions and their graphs. These activities will look into the function's zeros, and horizontal and vertical asymptotes. It contains a number of interesting critical thinking questions that take your pupils beyond the graph and into a deeper understanding of the graph.