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Lesson Planet

#### 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...

Lesson Planet

#### 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.

Lesson Planet

#### Proof: cos(a+b)=(cos a)(cos b)-(sin a)(sin b)

Using a similar method that he used to prove the sum of angles formula for sine, Sal shows the proof of the cosine sum of angles formula, cos (a+ b) = cos (a) cos (b) - sin (a) sin (b). This proof also uses the SOH-CAH-TOA model and some...

Lesson Planet

#### Proof: A(logB) = log (B^A), log A - log B = log (A/B)

Here the proofs for two logarithm properties are shown. First, the Power Property of Logarithms is proved using the definition of a logarithm and the rules of exponents and then, the Quotient Property is proved is a similar fashion.

Lesson Planet

#### Polar Coordinates 1

In this introductory video, Sal defines polar coordinates and using basic trigonometry identities and the Pythagorean Theorem defines the relationships between Cartesian coordinates and polar coordinates.

Lesson Planet

#### Patterns in Sequences 2

This video looks again at finding the algebraic pattern in sequences. In the example, we are looking at a figure where a number of toothpicks (or lines) are added each time, and you need to find how many toothpicks will be in the 50th...

Lesson Planet

#### Patterns in Sequences 1

Faced with a series of numbers we need to find the next few values of the sequence. This short video shows an example of finding the next values in a sequence where we need to find the pattern of adding a specific number each time to...

Lesson Planet

#### Parallel Lines 2

Can you tell, algebraically, if three lines are parallel? In this video, Sal demonstrates how to rewrite linear equations in slope-intercept form and compare the slope of each line.

Lesson Planet

#### Parabola Focus and Directrix 1

Starting with a point (focus) and a line below the point (directrix), in this video, Sal tries to find the set of all points (locus) equidistant to the point and the line. He shows, using the distance formula, that indeed, we have an...

Lesson Planet

#### Introduction to Logarithms Properties

Sal gets to the heart of the matter in this video, clarifying that it's important to understand math "so you can actually apply it in life later on and not have relearn everything every time." True to his word, Sal demonstrates ways to...

Lesson Planet

#### 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...

Lesson Planet

#### Introduction to Interest

Here is a simple tutorial on the difference between simple and compound interest. In it, Sal describes what interest is, defines the vocabulary of principle and interest rate. He also models year-by-year the amount of money owed under...

Lesson Planet

#### Introduction to Function Inverses

Starting from a brief look at functions and the mapping of domains to ranges, Sal starts out with an intuitive sense of what a function inverse is. He then, using an example, shows how to find the inverse of a function and also shows how...

Lesson Planet

#### Intro to 30-60-90 Triangles

As the fourth part of a series on the Pythagorean Theorem, Sal continues an exploration of the ways to calculate the length of sides of a right triangle using algebra. He also explores using this theorem to solve problems involving a...

Lesson Planet

#### Identifying Conics 2

In this video, Sal shows again how to write an equation of a conic section in standard form and identify the conic section it represents. This time, his example is of a hyperbola (not centered at the origin), which he also graphs.

Lesson Planet

#### Identifying Conics 1

After watching this video, you should be able to write an equation of a conic section in standard form, and identify the conic section from its equation. In an example problem, Sal reviews how to complete the square and graph an ellipse...