# Calculus Differentiation Teacher Resources

Find Calculus Differentiation lesson plans and worksheets
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#### AP Calculus AB

For Students 11th - 12th
Prepare high school mathematicians for the AP Calculus AB exam with a collection of 38 videos that can be used to introduce the topics or as a review. The videos focus on two processes; differentiating a function and integrating a...
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#### AP Calculus AB Unit 7: Differential Equations

For Teachers 11th - 12th
As with the other units in the Flipped Classroom Calculus course, the Differential Equations Unit follows the College Board’s course and exam description. Topics are introduced with an instructional video demonstrating how to approach...
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#### Differentiation Computations

For Students 11th
In this calculus instructional activity, 11th graders solve problems using differential equations and computations. They apply properties of trig functions and simplify their answers. There are 9 questions.
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#### Reductions of Order

For Students 11th - 12th
In this calculus worksheet, students identify functions as linear or nonlinear, homogeneous versus nonhomogeneous by using the reduction power theorem. There are 5 questions.
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#### Differential Equations Representing Growth and Decay: Rice Legend

For Students 11th - Higher Ed
The legend of a wise man who asks a king for rice as a reward presents a context to study exponential solutions to differential equations. Pupils move quantities of rice to a chessboard and calculate the amount of rice for each day. To...
9:50
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#### Calculus: Derivatives 3

For Students 11th - Higher Ed
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, "Calculus Derivatives 2Ó and...
9:02
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#### Calculus: Derivative of x^(x^x)

For Students 11th - Higher Ed
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 .
9:26
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#### Calculus: Derivatives 1

For Students 11th - Higher Ed
Sal defines the term derivative by taking the listener on a well-organized tour of slope. First, he reviews the concept of slope of a line from algebra, then extends this idea to look at the slope of the curve by first examining a secant...
11:05
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#### Calculus: Derivatives 2.5 (new HD version)

For Students 11th - Higher Ed
By defining the formal definition of a derivative, f(x), Sal is able to find the general form of the derivate function for the example f(x) = x2. He continues to stress the importance of an intuitive understanding of derivative functions.
9:30
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#### Calculus: Derivatives 2

For Students 11th - Higher Ed
Sal continues where he left off with the last video, "Derivatives 1,Ó by looking at the equation y = x^2 and examining the slope of the secant line at a specific point, and again defining the limit as x approaches zero to get the slope...
8:08
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#### Equation of a Tangent Line

For Students 11th - Higher Ed
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...
8:49
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#### Product Rule

For Students 11th - Higher Ed
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.
4:40
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#### Proof: d/dx(e^x) = e6x

For Students 11th - Higher Ed
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 "Proof of Derivatives of Ln(x) and e^x,Ó has a clearer explanation of this proof.
9:52
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#### Proof: d/dx(ln x)=1/x

For Students 11th - Higher Ed
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 "Proof of Derivatives of Ln(x) and e^x,Ó has a clearer explanation of this...
5:07
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#### Proof: d/dx(sqrt(x))

For Students 11th - Higher Ed
Using the definition of a limit, Sal proves the derivative of x or x1/2 is equal to _ x-1/2.
7:03
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#### Proof: d/dx(x^n)

For Students 11th - Higher Ed
Using the binomial theorem and definition of a limit, Sal shows a proof that the derivative of xn equals nxn-1.
8:58
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#### Limit Examples (Part 1)

For Students 11th - Higher Ed
One example, find the limit as x approaches -1 of (2x+2)/(x+1), is solved by simplifying the expression and then is explored intuitively by looking at the left and right-hand limit. The second example of finding the limit as x approaches...
11:32
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#### Introduction to Limits (HD)

For Students 11th - Higher Ed
Sal begins his explanation of limits with a few basic examples and takes a more intuitive point of view before looking at a formal mathematical definition in later videos. He starts by introducing the notation for limits and describes...
11:03
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#### Introduction to Limits (HD)

For Teachers 11th - Higher Ed
Sal begins his explanation of limits with a few basic examples and takes a more intuitive point of view before looking at a formal mathematical definition in later videos. He starts by introducing the notation for limits and describes...
7:39
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#### Introduction to Limits

For Students 11th - Higher Ed
Sal starts an explanation of limits by looking at a basic example of a discontinuous function and takes a more intuitive point of view before looking at a formal mathematical definition in later videos.  He starts by introducing the...
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#### Worksheet 31

For Students 12th - Higher Ed
In this math worksheet, students find the solutions to the differential equations. They also investigate the application of recognizing the parts of the equation.
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#### Worksheet 30

For Students 11th - Higher Ed
In this math instructional activity, students solve the differential equation by means of a power series about the point x0 = 2. Then they find the recurrence relation and the first four terms.
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#### Worksheet 20

For Students 10th - 12th
In this math activity, they write down and solve a differential equation governing the motion of an underdamped spring. Then they find the solution to the initial value problem.
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#### Worksheet 13

For Students 11th - Higher Ed
For this math worksheet, students find the solution for the Euler equation. Then they simplify the two differential for the functions of g and yp.