The 14 videos in this collection focus on all aspects of Differentiation, from maxima and minima to the chain, product and quotient rule.

Running Time

328 mins

Nb videos

14 videos included

Kanopy ID

1106121

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Differentiation From First Principles

What is differentiation? It is about rates of change -- for example, the slope of a line is the rate of change of y with respect to x. To find…

Differentiating Powers of x

If y=x^n then dy/dx = nx^n-1. This result is derived in this unit and illustrated with several examples, including cases where n is negative, or is a fraction.

Differentiating Sines and Cosines

This unit covers the differentiation of sin x and cos x from first principles.

Differentiating Logs and Exponentials

This unit gives details of how logarithmic functions (ln x) and exponential functions (e^x) are differentiated.

Using a Table of Derivatives

The construction of a Table of Derivatives of common functions using differentiation from first principles. Linearity rules for constant multiples of functions and for sum/difference of two functions, with examples,…

The Quotient Rule

A special rule, the quotient rule, may be used to differentiate the quotient of two functions.

The Product Rule

A special rule, the product rule, may be used to differentiate the product of two (or more) functions.

The Chain Rule

A special rule, the chain rule, may be used to differentiate a composite function (that is, a function of another function).

Parametric Differentiation

Instead of a function y(x) being defined explicitly in terms of the independent variable x, it is sometimes useful to define both x and y in terms of a third…

Differentiation by Taking Logarithms

The logarithm of a product is a sum, and so logarithms can be used to simplify certain functions for the purpose of differentiation.

Implicit Differentiation

Sometimes functions are not given in the form y = f(x) but in a more complicated form where it is difficult to express y explicitly in terms of x. These…

Extending the Table of Derivatives

In this unit the Table of Derivatives continues to be built using rules described in other units.

Tangents and Normals

This unit explains how differentiation can be used to calculate the equations of the tangent and normal to a curve. The tangent is a straight line which just touches the…

Maxima and Minima

Because the derivative provides information about the gradient of a graph of a function, we can use it to locate points on a graph where the gradient is zero. Such…

Integration

The 11 videos in this collection focus on all aspects of Integration, from integration as summation to integration leading to log functions.

Moments

A compilation of the following programs: Doors, heart valves & flic-flacs, Circular Motion, Modelling forces - sliding and toppling, Differentiation of vectors - radial and transverse components (tutorial), Differentiation of Vectors (tutorial) and Combining vectors pt 2 (tutorial).

Moving Bodies with Constant Mass

A compilation of the following programs: : Deceleration with parachutes, Acceleration with planes, Bows and Arrows, Differentiation of natural log of x (tutorial), Inverse Trig function - differentiation (tutorial), Exponential Functions (tutorial), Integrals that lead to log functions (tutorial), Integration by substitution (tutorial), Partial Fractions (tutorial) and Differential Equations -…

Vectors

A compilation of the following programs: Kites, Angular Momentum, Vectors and Moments, Modelling with 3D vectors, Introduction to Vectors (tutorial), Cartesian representation of vectors in 3D space (tutorial), Combining vectors pt 1 and 2 (tutorials) and Differentiation of vectors (tutorial).

Marketing Mix: Product

Key topics explored in this video series include:

- Value Analysis
- Product Life Cycle
- Product Portfolio
- Boston Matrix
- Product Differentiation
- Brand Extension/Product Extension
- An exploration of what most marketers would regard as the most important element of the Marketing Mix: Product.

Functions and Graphs

The 8 videos in this collection focus on all aspects of Functions and Graphs.

Algebra

The 18 videos in this collection focus on all aspects of Algebra, from logarithms to quadratic equations and partial fractions.

Arithmetic

The 8 videos in this collection focus on all aspects of Arithmetic, from fractions to percentages and ratios.

Geometry and Vectors

The 10 videos in this collection focus on all aspects of Geometry and Vectors.

L'Hospital's Rule

This program covers the important topic of L'Hospital's Rule in Calculus. We begin by discussing what L'Hospital's Rule is, how it is used to take derivatives, and why it is a central topic in Calculus. Next, we solve several practical calculus problems that give students practice with L'Hospital's Rule. The…

The Joy of Differential Calculus

Calculus is the mathematics of change, and answers questions such as: How fast is a function growing? This lecture introduces the concepts of limits and derivatives, which allow the slope of a curve to be measured at any point.

Expert Backgammon

Mathematically trained players also have a decisive edge in backgammon, which trains you to make decisions in highly uncertain conditions. Professor Benjamin explains the rules of the game, the basic strategies for winning, the best ways to play your opening rolls, and how math constantly enters the picture--from figuring out…

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