Constant Rule Teacher Resources
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Calculus: Derivatives 3
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.
10 mins 11th - Higher Ed Math
L'Hopital's Rule Example 2
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.
5 mins 11th - Higher Ed Math
Proofs of Derivatives of Ln(x) and e6x
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.
12 mins 11th - Higher Ed Math
Equation of a tangent line
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.
8 mins 11th - Higher Ed Math
Graph And Their Derived Function
Learners 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.
10th - 12th Math
Drip, Drop, Drip, Drop
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.
6th - 9th Math
Graphs of Functions and Their Derivatives
Students 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.
9th - 12th Math
Time Constant Calculations
In this time constant worksheet, students answer 52 questions about the rate of current changes and voltage changes in capacitors. They analyze circuits and determine the time it takes for capacitors to change voltage and they specify voltages at specified times.
10th - Higher Ed Science
AP Calculus Practice Exam
In this Calculus instructional activity, 12th graders are provided with practice problems for their exam. Topics covered include limits, derivatives, area bounded by a curve, minimization of cost, and the volume of a solid of revolution. The four page document contains seventeen multiple choice questions.