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Difference Rule Teacher Resources
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Sal shows the complex solution to a challenging derivative problem about ï¿½normalinesï¿½. This is probably beyond the scope of most first year calculus students but might be an interesting problem to show how complex these problems can get. Most of the thorny computations shown utilize techniques learned in algebra, but the notation used and the multifaceted parts of the problem make it quite involved.
Continuing to use the chain rule, Sal shows more examples of finding the derivative, this time, by looking at composite functions. Note: The current set of practice problems titled ï¿½Chain rule 1ï¿½ cannot be solved until one knows how to find the derivative of ex and trigonometric functions
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.
Students construct the graph of derivatives using a tangent line. In this construction of a graph of a derivative lesson plan, 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.
Pupils practice the concept of graphing associated to a function with its derivative. They define the concepts of increasing and decreasing function behavior and explore graphical and symbolic designs to show why the derivative can be used as an indicator for the behavior.
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.
This video covers the differential notation dy/dx and generalizes the rule for finding the derivative of any polynomial. It also extends the notion of the derivatives covered in the Khan Academy videos, ï¿½Calculus Derivatives 2ï¿½ and ï¿½Calculus Derivatives 2.5 (HD).ï¿½ Note: Additional practice using the power rule for differentiating polynomials (including some with negative exponents) is available to the listener.
Twelfth graders explore differential equations. In this calculus instructional activity, 12th graders explore Euler’s Methods of solving differential equations. Students use the symbolic capacity of the TI-89 to compare Euler’s Method of numeric solutions to a graphical solution.
In this calculus worksheet, 12th graders differentiate and integrate basic trigonometric functions, calculate rates of change, and integrate by substitution and by parts. The twenty-two page worksheet contains explanation of the topic, numerous worked examples, and sixteen multi-part practice problems. Answers are not provided.
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.