# Calculus Differentiation Teacher Resources

Find Calculus Differentiation lesson plans and worksheets

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#### Differentiation Computations

In this calculus 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

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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#### Worksheet 31

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 this math worksheet, 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

In this math worksheet, 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

In this math worksheet, students find the solution for the Euler equation. Then they simplify the two differential for the functions of g and yp.

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#### Worksheet 3

in this math instructional activity, students define the meaning of a differential equation. Then they examine the method of solving a separable equation.

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#### Worksheet 14 Spring 1996

In this math learning exercise, students answer the questions in the context of either being true or false. The topics covered include derivatives and differential equations.

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#### The Method of Separation of Variables

In this math worksheet, students read the examples of the initial value problems. Then they write all the possible solutions for the differential equation.

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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: 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 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)

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

By defining the formal definition of a derivative, fï¿½(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...

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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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#### Extreme Derivative Word Problem (advanced)

Sal shows the complex solution to a challenging derivative problem about ï¿½normalinesï¿½. This is probably beyond the scope of most first year calculus students but might be an interesting problem to show how complex these problems can...

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

Using the definition of a limit, Sal proves the derivative of ï¿½x or x1/2 is equal to _ x-1/2.

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#### L'Hopital's Rule Example 3

In this video, Sal starts with an example where the limit is not indeterminate but rather undefined and therefore cannot be solved using L'Hoptial's rule. He shows how you can rewrite the problem algebraically so that the rule can be...

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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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#### Introduction to L'Hopital's Rule

After defining L'Hopital's rule, Sal shows an example of using the rule to solve for the limit as x approaches 0 of (sin x) / x. He also describes what it means for a fraction to have indeterminate form.

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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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#### L'Hopital's Rule Example 1

After applying L'Hopital's Rule once and showing that the limit is still indeterminate, Sal applies the rule a second and third time before arriving at a limit that exists. He then shows that given that the final limit exists, so do the...