

Properties of the Derivatives of Vector Valued Functions
Welcome to a review of the properties of the derivative of a vectorvalued function, part one. In this video, we’ll take a look at proving the property involving the derivative of a dot product. So here we have the six properties of the derivative of a vectorvalued function we’re gonna take a look at. These will look very familiar to some of the properties that we reviewed when we were finding derivatives of basic functions. This first property just states that if we want to find the derivative of a constant times a vectorvalued function R of T, that’ll just equal the constant times the derivative of that vectorvalued function.…

Properties of Limits Calculus 1 AB
BAM!!! Mr. Tarrou. That was a quite jump. In this video we are going to continue our discussion of limits. The basic idea of limits and how you find them in Calculus. So I just did a video of finding limits both graphically and numerically. That is just looking at graphs of functions and identifying limits, both the left and the right hand limits. If those are equal then there is a two sided limit. And finding them with ttable. But both of those techniques are very tedious. Now we are going to start looking at properties of limits and learning how we can just use algebra, and not have…

Ex 2: The Distributive Property
– HERE ARE SOME MORE EXAMPLES OF USING THE DISTRIBUTIVE PROPERTY TO SIMPLIFY EXPRESSIONS. IN THE FIRST EXAMPLE WE HAVE 9P x THE QUANTITY P + 2. SO, WE WANT TO DISTRIBUTE 9P, WHICH MEANS WE WANT TO MULTIPLY 9P AND P AS WELL AS 9P AND 2. SO, WE’D HAVE 9P x P + 9 x 2. WELL, 9P x P IS GOING TO BE 9P TO THE SECOND OR 9P SQUARED, AND THEN WE’LL HAVE + (18), BUT INSTEAD OF LEAVING IT IN THIS FORM AS + AND , IT’S MORE COMMON TO WRITE THIS AS SUBTRACTING A POSITIVE. SO, THIS IS EQUIVALENT TO 9P SQUARED – (+18).…

PreAlgebra 7 – Associative & Distributive Properties of Multiplication
Hello. I’m Professor Von Schmohawk and welcome to Why U. In our last lecture we saw that addition and multiplication are both commutative operations. The order of numbers which are added or multiplied can be rearranged without affecting the result. As we saw, addition also has an “associative” property. According to the Associative Property of Addition three or more numbers which are added can be grouped in any way without affecting the result. Does this also apply to multiplication? Let’s start with our stack of 24 boxes and group them in different ways before multiplying. For instance if we group the two and the three we get four groups of…

Properties of Exponents
– WELCOME TO THE PRESENTATION ON THE PROPERTIES OF EXPONENTS. THE GOAL OF THIS VIDEO IS TO USE THE PROPERTIES OF EXPONENTS TO SIMPLIFY EXPRESSIONS. HERE IS A LIST OF THE PROPERTIES OF EXPONENTS WE WILL BE DISCUSSING TODAY. YOU MAY WANT TO PAUSE THE VIDEO NOW AND WRITE THESE DOWN. WE WILL CONSIDER THEM ONE AT A TIME. THE FIRST PROPERTY IS A PRODUCT PROPERTY. IT STATES IF YOU’RE MULTIPLYING AND THE BASES ARE THE SAME, YOU ADD THE EXPONENTS. LET’S TAKE A LOOK AT WHY THAT MAKES SENSE. IF WE WANT TO MULTIPLY 5 TO THE SECOND x 5 TO THE FOURTH, WE KNOW THAT 5 TO THE…

The Properties of Logarithms
– WELCOME TO OUR LESSON ON THE PROPERTIES OF LOGARITHMS. LET’S GO AHEAD AND GET STARTED. THE FIRST PROPERTY IS LOG BASE A OF 1 IS EQUAL TO ZERO AND THIS IS TRUE BECAUSE A TO THE POWER OF ZERO WILL ALWAYS EQUAL 1. AND IF WE WANT AN EXAMPLE OF THIS WE COULD SAY LOG 1 OF ANY BASE, LET’S JUST SAY 8, WILL ALWAYS EQUAL ZERO BECAUSE 8 TO THE ZERO IS EQUAL TO 1. PROPERTY 2 SAYS LOG BASE A OF A IS EQUAL TO 1 SINCE A TO THE POWER OF 1 WILL EQUAL A SO IF THE BASE AND THE NUMBER ARE THE SAME IT…

Ex 1: The Distributive Property
– WE WANT TO USE THE DISTRIBUTIVE PROPERTY TO SIMPLIFY THE GIVEN EXPRESSIONS. SO, HERE WE HAVE 5 x THE QUANTITY X + 2. SO, WE NEED TO MULTIPLY THE 5 AND THE X AS WELL AS THE 5 AND THE 2, AND SOMETIMES YOU’LL HEAR DISTRIBUTION REFERRED TO AS MULTIPLICATION ACROSS ADDITION OR SUBTRACTION, AND THIS IS WHY. SO, WE’LL HAVE 5 x X + 5 x 2. WELL, 5 x X WOULD BE 5X, AND 5 x 2=10. SO, WE HAVE 5X + 10. IN THE SECOND EXAMPLE WE’RE DISTRIBUTING +3. SO WE’LL HAVE +3 x X – +3 x 9. SO WE’LL HAVE 3 x X –…

PreAlgebra 6 – Commutative Property of Multiplication
Hello. I’m Professor Von Schmohawk and welcome to Why U. In our last lecture, we saw how the people on my primitive island of Cocoloco discovered addition and subtraction. Once we had invented addition and subtraction the Cocoloconians could calculate very complicated coconut transactions with great precision. But we soon found out that with only addition and subtraction some calculations could take a very long time. For instance, once a year, everyone on Cocoloco must donate three coconuts for the annual feast of Mombozo. So if all 87 inhabitants of Cocoloco each donate three coconuts then how many coconuts will we have for the feast? Before we discovered multiplication, we…

Ex: Simplify Exponential Expressions Using Power Property – Products to Powers
We want to simplify the following expressions completely. The first expression is two x raised to the fourth power. Let’s first simplify this by expanding, and then we’ll simplify it again using the power property of exponents. Notice we have an exponent of four, which means we have four factors of the base, which is two x. So this is equal to two x, times two x, times two x, times two x. Once expanded, notice how we can see we have four factors of two and four factors of x, so we can write this as two to the fourth times x to the fourth, and we can evaluate…