Calculus Differentiation Teacher Resources

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.

In this calculus activity, students identify functions as linear or nonlinear, homogeneous versus nonhomogeneous by using the reduction power theorem. There are 5 questions.

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...

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...

Sal starts by showing how to find dy/dx of y = x2 and then moves on to show the solution to the more complicated implicit differentiation problem of finding the derivative of y in terms of x of y = x ^ x ^ x.

Sal defines the product rule and then shows two examples of its use. He then shows an example of finding the derivative using the chain and product rules together.

By defining the formal definition of a derivative, f(x), Sal can 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.

Using the definition of a limit, Sal proves that the derivative of x or x1/2 equals _ x-1/2.

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...

Sal defines the term derivative by taking the listener on a well-organized tour of the slope. First, he reviews the concept of the slope of a line from algebra, then extends this idea to look at the slope of the curve by first examining...

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 second line at a specific point, and again defining the limit as x approaches zero to get the slope...

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...

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...

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...

Using the derivative of ln x, the chain rule, and the definition of a limit, Sal shows proof that the derivative of ex = ex. Note: The video titled "Proof of Derivatives of Ln(x) and e^x,Ó clearly explains this proof.

Using the definition of a limit, various properties of logarithms, and a definition of e, Sal shows the proof of the derivative of ln x = 1/x. Note: The video titled "Proof of Derivatives of Ln(x) and e^x,Ó has a more straightforward...

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

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...

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.

In this math worksheet, learners 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.

In this math learning exercise, 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.

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.