Difference 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 4 Views 2 Downloads
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 3 Views 0 Downloads
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.
10 mins 11th - Higher Ed Math 3 Views 0 Downloads
Twelfth graders investigate derivatives. In this calculus lesson, 12th graders use technology to explore the basic derivatives and how to choose the proper formula to use them. The lesson requires the use of the TI-89 or Voyage and the appropriate application.
12th Math 3 Views 13 Downloads
Proof: d/dx(ln x)=1/x
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.
10 mins 11th - Higher Ed Math 3 Views 0 Downloads
In this calculus worksheet, 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.
12th - Higher Ed Math 5 Views 58 Downloads
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 3 Views 0 Downloads
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.
11th - 12th Math 3 Views 14 Downloads
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 3 Views 29 Downloads
Graph And Their Derived Function
Students 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 4 Views 25 Downloads
Why we Use Theorem In Calculus
Students 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.
12th - Higher Ed Math 3 Views 20 Downloads
Review of Calculus BC II
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.
11th - 12th Math 3 Views 3 Downloads
Implicit Differentiation on the TI-89
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.
12th - Higher Ed Math 3 Views 4 Downloads
Surfing the Waves
Young scholars 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.
9th - 12th Math 3 Views 11 Downloads
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 3 Views 88 Downloads
Functions and Velocity
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.
9th - 11th Math 3 Views 8 Downloads