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Differentiation from first principlesAfter reading this text, and/or viewing
the video tutorial on this topic, you should be able to
understand the process involved in differentiating from first principles and
differentiate some simple functions from first principles.
Cosecant, Secant and CotangentThis unit explains what is meant by these three trigonometric ratios.
Graphs of the corresponding functions are provided.
Differentiation by taking logsIn this unit we look at how we can use logarithms to simplify certain functions before we differentiate them. (Mathtutor Video Tutorial)
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
Differentiation by taking logsIn this unit we look at how we can use logarithms to simplify certain functions before we differentiate them. (Mathtutor Video Tutorial)
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
Trigonometric equationsThis workbook explains how a number of trigonometric equations can be solved by making reference to a Table of standard results and using the symmetries and periodicities present in the graphs of trig functions.
Differentiation by taking logarithmsIn this unit we look at how we can use
logarithms to simplify certain functions before we differentiate them.
Integration that leads to logarithmsThe derivative of ln x is 1/x. As a consequence, if we reverse
the process, the integral of 1/x is ln x+c. In this unit we
generalise this result and see how a wide variety of integrals result in
logarithm functions.
The exponential constant eThe letter e is used in many mathematical calculations to stand for a particular number known as the exponential constant. This leaflet provides information about this important constant, and the related exponential function.
Differentiating sin(x) and cos(x) from first principlesIn this unit we show how to differentiate the sine and cosine functions
from first principles. (Mathtutor Video Tutorial).
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
Differentiating sin(x) and cos(x) from first principlesIn this unit we show how to differentiate the sine and cosine functions
from first principles. (Mathtutor Video Tutorial).
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
Table of derivativesThis leaflet provides a table of common functions and their derivatives, and the opportunity to practice using it.
Differentiation for Economics and Business Studies Functions of One VariableOverview of differentiation and its applications in Economics. This leaflet has been contributed to the mathcentre Community Project by Morgiane Richard (University of Aberdeen) and reviewed by Anthony Cronin (University College Dublin).
Linearity rulesThere are two rules known as linearity rules which, when used with a table of derivatives, enable us to differentiate a wider range of functions. These rules are summarised in this leaflet.
The Product RuleA special rule, the product rule, exists for differentiating products of two (or more) functions. This unit illustrates this rule. (Mathtutor Video Tutorial)
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
The Quotient RuleA special rule, the quotient rule, exists for differentiating quotients of
two functions. This unit illustrates
this rule. (Mathtutor Video Tutorial)
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
Integration by partsA special rule, integration by parts, is available for integrating
products of two functions. This unit derives and illustrates this rule with a
number of examples.
The double angle formulaeDouble angle formulae are so called because they involve trigonometric functions of double angles e.g. sin 2A, cos 2A and tan 2A. (Mathtutor Video Tutorial)
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
The logarithm functionThis leaflet provides a table of values and a graph of the logarithm function. (Engineering Maths First Aid Kit 3.7)
Product Rule Practice - Numbas10 questions on the product rule in differentiation. Numbas resources have been made available under a Creative Commons licence by Bill Foster and Christian Perfect, School of Mathematics & Statistics at Newcastle University.
Quotient rule practice - Numbas8 questions on the quotient rule in differentiation. Numbas resources have been made available under a Creative Commons licence by Bill Foster and Christian Perfect, School of Mathematics & Statistics at Newcastle University.
Exponential and Logarithm for Economics and Business StudiesOverview of the properties of the functions e and ln and their applications in Economics. This leaflet has been contributed to the mathcentre Community Project by Morgiane Richard (University of Aberdeen) and reviewed by Shazia Ahmed (University of Glasgow) and Anthony Cronin (University College Dublin).
The Product RuleA special rule, the product rule, exists for differentiating products of two (or more) functions. This unit illustrates this rule. (Mathtutor Video Tutorial)
The video is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
The Quotient RuleA special rule, the quotient rule, exists for differentiating quotients of
two functions. This unit illustrates
this rule. (Mathtutor Video Tutorial)
The video is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
Integration by partsA special rule, integration by parts, is available for integrating
products of two functions. This unit derives and illustrates this rule with a
number of examples. (Mathtutor Video Tutorial)
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
The double angle formulaeDouble angle formulae are so called because they involve trigonometric functions of double angles e.g. sin 2A, cos 2A and tan 2A. (Mathtutor Video Tutorial)
The video is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
