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30 resources with the concept defferentiable

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.
7:50
Lesson Planet

L'Hopital's Rule Example 3

For Students 11th - Higher Ed
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...
5:16
Lesson Planet

L'Hopital's Rule Example 2

For Students 11th - Higher Ed
Sal shows two different ways of finding the limit of a rational expression where the limit of the polynomial is of an indeterminate form involving infinity. First, he shows how to solve this using L�Hopital�s Rule and then by using the...
7:43
Lesson Planet

L'Hopital's Rule Example 1

For Students 11th - Higher Ed
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...
8:52
Lesson Planet

Introduction to L'Hopital's Rule

For Students 11th - Higher Ed
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.
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.
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...
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 .
9:02
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 .
3:56
Lesson Planet

Extreme Derivative Word Problem (advanced)

For Students 11th - Higher Ed
Sal shows the complex solution to a challenging derivative problem about �normalines�. 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...
3:56
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...
5:08
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.
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.
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...
Lesson Planet

Worksheet One - Definite Integral

For Teachers Higher Ed
In this definite integral worksheet, students use substitution to simplify integrals. They find the values of the upper and lower points and interpret points found on a graph. Students solve this two-page worksheet.
Lesson Planet

Worksheet 32 - Antiderivative

For Teachers Higher Ed
In this antiderivative worksheet, students determine the antiderivative by using substitution. They evaluate integrals. This one-page worksheet contains approximately six multi-step problems.
Lesson Planet

At Home

For Teachers K - 1st
As part of a vocabulary development exercise (perfect for ELD) about "At Home," learners count from 20-29 by 1s and skip count by 10s to 100. They label a poster of a house with proper vocabulary words. Ideas for differentiating among...
Lesson Planet

Derivatives

For Students 10th - 12th
In this derivatives instructional activity, students identify intervals. They differentiate given functions. This one page instructional activity contains seven multi-step problems.
Lesson Planet

Differentiating Special Functions

For Students 11th - 12th
For this differentiating special functions worksheet, students solve and complete 5 various types of problems. First, they differentiate each of the given functions. Then, students complete the table using a calculator and plot the...