Difference Rule Teacher Resources
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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.
Sal defines the product rule and then shows two examples of how it is used. He then shows an example of finding the derivative by using both the chain rule and product rule together.
In this video, Sal takes on the challenge of proving both the derivative of ln x = 1/x and of ex = ex, showing that no circular logic is used in the proof. It contains a clearer version of both proofs shown in the videos titled, _Proof d/dx e^x = e^x” and _Proof: d/dx (ln x) = 1/x.”
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.
Twelfth graders investigate derivatives. In this calculus instructional activity, 12th graders use technology to explore the basic derivatives and how to choose the proper formula to use them. The instructional activity requires the use of the TI-89 or Voyage and the appropriate application.
Using the definition of a limit, various properties of logarithms, and a definition of e, Sal shows the proof of derivative of ln x = 1/x. Note: The video titled ï¿½Proof of Derivatives of Ln(x) and e^x,ï¿½ has a clearer explanation of this proof.
In this calculus activity, students find the derivative of a function. They use the product rule to to differentiate each problem. There are 21 problems with an answer key.
In this calculus worksheet, students solve functions using the derivative formulas. There are 26 formulas for them to review and go over.
In this calculus activity, students 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.
Sal shows two different ways of finding the limit of a rational expression where the limit of the polynomial is of an indeterminate form involving infinity. First, he shows how to solve this using Lï¿½Hopitalï¿½s Rule and then by using the factoring method to solve for the limit algebraically. Note: Practice problems on Lï¿½Hopitalï¿½s rule are available and can be practiced now or after watching the other example videos.
Students construct the graph of derivatives using a tangent line. In 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.
High schoolers 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.
Young scholars analyze graphs and determine their general shape. In this calculus lesson, students solve functions by taking the derivative, sketch tangent lines and estimate the slope of the line using the derivative. They graph and analyze their answers.
Young scholars read an article to explain the reasoning behind theorems. In this calculus lesson, students understand the underlying principles of theorems and how it helps them make sense of the problems. They know why they do what they do in AP Calculus.
In this Calculus learning exercise, 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 learning exercise contains fifty-two problems. Answers are not provided.
In this calculus worksheet, students use integration to solve word problems they differentiate between integration and anti derivatives, and between definite and indefinite integrals. There are 3 questions with an answer key.
Students analyze implicit differentiation using technology. In this calculus lesson, students solve functions dealing with implicit differentiation on the TI using specific keys. They explore the correct form to solve these equations.
Students use online resources, including animations,to define the slope of a curve and how to calculate the slope. They solve 8 problems online, using the definition of the derivative of a function at a point to calculate slope of the curve.
Design an experiment to model a leaky faucet and determine the amount of water wasted due to the leak. Middle schoolers graph and write an equation for a line of best fit. They use their derived equation to make predictions about the amount of water that whould be wasted from one leak over a long period of time or the amount wasted by serveral leaks during a specific time period.
Young scholars calculate the velocity of object as they land or take off. In this calculus lesson, students are taught how to find the velocity based on the derivative. They graph a picture the represent the scenario and solve for the velocity.