Differentiation Teacher Resources
Find Differentiation educational ideas and activities
Showing 1 - 20 of 106 resources
Calculus: Derivative of x^(x^x)
Sal starts with an example of finding dy/dx of y = x2 and builds to showing the solution to the more complicated implicit differentiation problem of finding the derivative of y in terms of x of y = x ^ x ^ 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.
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.
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 2.5 (HD).ï¿½ Note: Additional practice using the power rule for differentiating polynomials (including some with negative exponents) is available to the listener.
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.
Calculus and the TI-89
Students investigate calculus using the TI Calculator. In this calculus lesson, students deepen their understanding of calculus. This lesson includes step by step instruction for the TI.
Approxiamte Solutions to Differential Equations-Slope Fields (graphical) and Euler's Method (numeric)
Twelfth graders explore differential equations. In this calculus lesson, 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.
The Ares-V Cargo Rocket
In this Ares-V cargo rocket worksheet, students read about this multi-purpose launch vehicle and its rocket boosters. Students are given an equation that relates the acceleration of the rocket to the time and mass of the rocket. They graph the thrust curve and mass curve, they graph the acceleration and they determine the rocket's absolute maximum in a given interval.
Twelfth graders investigate logarithm differentiation. In this calculus lesson, 12th graders explore situations in which one would use logarithmic differentiation as an appropriate method of solution. Students should have already studied the chain rule.
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.
Passive Integrator and Differentiator Circuits
In this circuits worksheet, students answer 25 questions about passive integrator circuits and passive differentiator circuits given schematics showing voltage. Students use calculus to solve the problems.
The Fundamental Theorems of Calculus
Are your calculus pupils aware that they are standing on the shoulders of giants? This lesson provides a big picture view of the connection between differential and integral calculus and throws in a bit of history, as well. Note: The calculus controversy paper is not included but one can find a number of good resources on the Internet regarding the development of calculus and the role of Newton and Leibnez.
AP Calculus Practice Exam
In this calculus worksheet, students calculate the derivative, find the invertible given the derivative and review basic concepts for their AP calculus exam. There are 17 questions.
Proof: d/dx(e^x) = e6x
Using the derivative of ln x, the chain rule, and the definition of a limit, Sal shows a proof that derivative of ex = ex. Note: The video titled ï¿½Proof of Derivatives of Ln(x) and e^x,ï¿½ has a clearer explanation of this proof.
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. It also, provides a nice visual understanding of the problem by graphing both the original equation and the found tangent line.
Integration By Parts
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.
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.
Even More Calculus
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.
Differentiation Using the Chain Rule
In this calculus worksheet, students solve problems using differentiation and the chain rules. They take the derivatives of equations using specific equations. There are 21 problems with an answer key.
Calculus at the Battle of Trafalgar
Students read an article on how calculus is used in the real world. In this calculus lesson, students draw a correlation between the Battle of Trafalgar and calculus. The purpose of this article is the show everyday uses for calculus in the real world.