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This video looks at the start point for differentiation - namely, differentiation from first priniciples.
This video looks at the rules for differentiation which don't need require it to be done from first principles. Basic examples are shown and a discussion about how graphs use the notation to confuse people.
This video takes a look at differentiating negative powers. After a short recap on how to differentiate functions with positive powers, I look at the idea of what functions look like when the x value is on the denominator. and how this means the graph will not be defined at the point where x=0. Knowing this helps us know which points of the graph can and can't be differentiated. Moving on, I look at how to negative powers can be turned into positive powers and vice versa. Using this knowledge I show how we can differentiate any function with a positive and negative power.
This video looks at how to draw sketches for the graphs of derivative functions. This looks at how to look at the maximum and minimum points of a function and use this to help you locate crossing points on the graphs of derivative functions. It then moves on to look at how to look at the values of gradients to then complete the graphs of derivative functions.
This video shows how to use the Chain Rule to differentiate functions. In previous lessons, we found that we could differentiate individual terms, but what happens when we have a number of terms multiplied together? We can use the chain rule to split the function into two separate functions and then combine them. This video shows the theory and then some practical examples of how to use the Chain Rule. So much fun!
This video takes a look at what Rational Powers are and how they are used in Mathematical Methods Units 3 and 4.
This video looks at how we can differentiate functions which take the form of y=e^x. This is part of the Mathematical Methods Units 3 and 4 course. I start by looking at why the differential of the function is the same as the function and then show how to use the chain rule to find the differential of more complex functions. A number of examples are covered and related back to the theory.
This video looks at how the formulae came to be for differentiating circular functions. It shows how they are used too. It's the whole circular functions package really.
This video shows how to use the Product Rule to differentiate functions.
This video shows how to use the Quotient Rule to differentiate functions. This video takes the time to look at how the quotient rule is and how it is used. We have already looked at the chain rile which shows how to split the product of terms and differentiate them. When we divide two functions we have to use another rule - the quotient rule. Much like the chain rule, there is a formula to use which makes the process really simple!
This video looks at limit notation and how it's used to help use describe continuity at a point.
This video is part of the Mathematical Methods Units 3 and 4 course. It looks at the conditions which are required for a function to be differentiable. There is also a look at what makes a function continuous. This is a pretty important part of this course.
This video is a return to the idea of the quotient rule but with circular functions. As the previous video was used to recap all the work for differentiation, this one is a lot shorter (YEA!). A quick example showing how the quotient rule works moves swiftly into two examples where we use the quotient rule with some circular function (or trig functions).
This video continues the work done with the product rule. It takes a trip down memory lane by revisiting the work on basic differentiation, through basic product rule and then one an example of how to use it with circular functions. There is also a quick discussion about the chain rule.
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These are the videos which are available in each chapter. You will notice that some are free and some are for subscribers only. Making and hosting these videos costs a little bit of money. To help pay for the hosting fees I have no choice but to hide some of the videos and make them for subscribers only.