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31 resources with the keyterm differential calculus

Videos (Over 2 Million Educational Videos Available)
Phonics Song 2 (new version) Video
2:54
Phonics Song 2 (new version)
Algebra 50 - Three Variable Systems in the Real World - Problem 2 Video
10:23
Algebra 50 - Three Variable Systems in the...
The Secret World of Animal Sleep 101 Sleepless on the Savanna Video
3:42
The Secret World of Animal Sleep 101...
Other Resource Types (31)
8:58
Lesson Planet

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...
9:44
Lesson Planet

Introduction to Rate-of-Change Problems

For Students 11th - Higher Ed
Sal solves an example for finding the rate of change of the height of water in a cone at a specific point when it is being filled at a given rate. In this video, Sal reviews the volume of a cone and the chain rule and then, uses these to...
9:37
Lesson Planet

Maxima Minima Slope Intuition

For Students 11th - Higher Ed
Before solving any problems, Sal gives an overview of what happens to the slope, first derivative, and second derivative at local maxima and minima to give the viewer a more intuitive feel for these types of problems.
9:49
Lesson Planet

Optimization Example 4

For Students 11th - Higher Ed
Sal does another optimization example, this time, minimizing the total cost of an open rectangular box. In this problem, the volume can be defined in terms of a single variable and given a cost model, he builds a cost equation. He finds...
9:44
Lesson Planet

Graphing with Calculus

For Students 11th - Higher Ed
In a problem where you are not given the original function, but rather only three known points on the graph and a few additional pieces of information about when the first and second derivatives are positive or negative, Sal shows how...
17:30
Lesson Planet

Optimization with Calculus 3

For Students 11th - Higher Ed
Using what one learned about finding the minimum and maximum of functions, the optimization problem to find two numbers whose product is -16 and whose sum of squares is a minimum is solved. Sal starts by writing the equations and...
18:05
Lesson Planet

Proof: lim (sin x)/x

For Students 11th - Higher Ed
By looking the expression (sin x)/x that is not defined at the limit value of 0, Sal uses the squeeze theorem to show that the function can by bound between two other functions that are defined at limit value so the limit can indeed be...
7:03
Lesson Planet

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.
5:07
Lesson Planet

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.
9:52
Lesson Planet

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...
4:40
Lesson Planet

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.
11:03
Lesson Planet

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...
8:08
Lesson Planet

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...
9:50
Lesson Planet

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...
9:30
Lesson Planet

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...
11:05
Lesson Planet

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.
8:28
Lesson Planet

Calculus: Derivatives 2 (new HD version)

For Students 11th - Higher Ed
Sal continues where he left off with the last video, "Derivatives 1,Ó by looking at the equation y = x2 and examining the slope of the secant line at a specific point. He continues with defining the limit as x approaches zero to get the...
9:26
Lesson Planet

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...
15:43
Lesson Planet

Calculus: Derivatives 1 (new HD version)

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...
9:02
Lesson Planet

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 .
9:07
Lesson Planet

Newton Leibniz and Usain Bolt

For Students 10th - 12th
What do Usain Bolt and calculus have in common? Using Usain Bolt as an example of distance traveled over a period of time, Sal shows why you need differential calculus to answer the question of how fast something is traveling at a...
16:48
Lesson Planet

Mean Value Theorem

For Students 11th - Higher Ed
Sal spends most this video explaining what the Mean Value Theorem says in a very intuitive way. He follows this with a concrete example of finding the value of a function on a closed interval where the slope is the same as the average...
12:27
Lesson Planet

Proofs of Derivatives of Ln(x) and e6x

For Students 11th - Higher Ed
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...
8:39
Lesson Planet

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,� has a clearer explanation of this proof.