# Calculus Differentiation Teacher Resources

Find Calculus Differentiation lesson plans and worksheets

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#### AP Calculus AB Unit 7: Differential Equations

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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#### AP Calculus AB

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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#### Differentiation Computations

In this calculus worksheet, 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

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

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...

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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, "Calculus Derivatives 2Ó and...

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#### 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 .

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#### Calculus: Derivatives 1

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...

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#### Calculus: Derivatives 2.5 (new HD version)

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.

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#### Calculus: Derivatives 2

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...

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#### 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...

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#### 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.

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#### 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 "Proof of Derivatives of Ln(x) and e^x,Ó has a clearer explanation of this proof.

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#### 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 "Proof of Derivatives of Ln(x) and e^x,Ó has a clearer explanation of this...

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#### Proof: d/dx(sqrt(x))

Using the definition of a limit, Sal proves the derivative of �x or x1/2 is equal to _ x-1/2.

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#### Proof: d/dx(x^n)

Using the binomial theorem and definition of a limit, Sal shows a proof that the derivative of xn equals nxn-1.

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#### Limit Examples (Part 1)

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...

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#### Introduction to Limits (HD)

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...

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#### Product Rule

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.

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#### 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...

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#### Introduction to Limits (HD)

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#### Introduction to Limits

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

In this math learning exercise, 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

In this math learning exercise, 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.