Differentiation

Differentiation is very helpful to determine how fast something changes. Slope and speed are defined by differentiation.

Context: rollercoaster

This video shows a rollercoaster as an example to explain the mathematical concept of differentiation. It introduces speed and slope, which can be defined using differentiation. 

Definition of derivative

The derivative is defined using speed and slope as examples. The process of determining the derivative is called differentiation. You will also learn about the tangent line.

How to determine the derivative?

This video show the grand plan for calculating derivatives: First, you learn the derivatives of the standard functions. Second: you learn rules to calculate the derivative of combinations of standard functions, such as the chain rule. Then you use the derivatives of the standard functions to obtain its derivative.

Rules of calculation for differentiation

Product rule for calculating the derivative of a function.

Rules of calculation for differentiation - part 2

Chain rule for calculating the derivatives of a function.

Derivatives of power functions

How do you calculate the derivative of power functions? In this video you will learn the general rule by looking at some examples.

Derivative of the sine

What is the derivative of the standard function sine? It is the cosine! Look at the graph of the sine and see why the cosine is the derivative of the sine.

Derivative of x^p and a^x

What is the derivative of the function x to the power p? And what is the derivative of the function a to the power x? We use the exponential function e^x to find the derivatives.

Non-differentiable functions

Can you differentiate any function at any point? The answer is "no". Why?

Tangent line

The derivative of a function is the slope of the tangent line at the graph of the function. In this video we will see how to find an equation of this tangent line.

Finding minima and maxima

How can you find the minima and maxima of a function using differentiation? This can help you to optimize the solutions to a problem. How can you find global and local maxima and minima? What is a boundary point, critical point and singular point?

First and second derivative test

To know the maximal or minimal values a function can have, you first have to find the critical points with the first derivative test. To see if a critical point is a local maximum or minimum you can use the second derivative test. This video shows you how!

Implicit differentiation

This video will prepare you for learning implicit differentiation. A technique to find the formula for the derivative without actually determining explicit formulas for the functions first.

Summary about differentiation

What is the definition of the derivative? How can you differentiate standard functions and other functions? This video gives the summary of week 5 of the edX course: pre-university Calculus (Calc001x).

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