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Differentiation from first principles resources

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Motivating Mathematics (2)

Faulty Tyres - David Saunders
This mathtutor extension discusses how mathematical modelling using differentiation may be used to determine optimum delivery sizes. This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
Millenium Bridge - James Robinson
This mathtutor extension describes the effect of resonance on bridges and how differential equations may be used to calculate the effects. This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Quick Reference (2)

Introduction to differentiation
This leaflet provides a rough and ready introduction to differentiation. This is a technique used to calculate the gradient, or slope, of a graph at different points.
Introduction to differentiation 8.1
This leaflet provides a rough and ready introduction to differentiation and gives some common terminology and notation. (Engineering Maths First Aid Kit 8.1) There is an accompanying podcast.

Teach Yourself (4)

Differentiating sin(x) and cos(x) from first principles
After reading this text, and/or viewing the video tutorial on this topic, you should be able to differentiate the functions sin(x)and cos(x) from first principles.
Differentiation from first principles
After 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.
Differentiation from first principles (powers of x)
This unit looks at some basic differentiation from first principles, and in particular how to differentiate powers of x.
Differentiation of the logarithm and exponential functions
In this unit the natural logarithm function and the exponential function are differentiated from first principles.

Test Yourself (4)

Diagnostic Test - Differentiating exp and log
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
Diagnostic Test - Differentiating x^n
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
Diagnostic Test - Differentiation from first principles
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
Exercise - Differentiating x^n
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Third Party Resources (2)

Mathematics Support Materials from the University of Plymouth
Support material from the University of Plymouth:
The output from this project is a library of portable, interactive, web based support packages to help students learn various mathematical ideas and techniques and to support classroom teaching.
There are support materials on ALGEBRA, GRAPHS, CALCULUS, and much more.
This material is offered through the mathcentre site courtesy of Dr Martin Lavelle and Dr Robin Horan from the University of Plymouth.
University of East Anglia (UEA) Interactive Mathematics and Statistics Resources
The Learning Enhancement Team at the University of East Anglia (UEA) has developed la series of interactive resources accessible via Prezi mind maps : Steps into Numeracy, Steps into Algebra, Steps into Trigonometry, Bridging between Algebra and Calculus, Steps into Calculus, Steps into Differential Equations, Steps into Statistics and Other Essential Skills.

Video (5)

Differentiating sin(x) and cos(x) from first principles
In 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.
Differentiation from first principles
In this unit we start to explain how differentiation works. The process is known as differentiation from first principles. (Mathtutor Video Tutorials) 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 from first principles (powers of x)
In this unit we explain how to differentiate powers of x from first principles. (Mathtutor Video Tutorials) 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 of the logarithm and exponential functions
This unit gives details of how logarithmic functions and exponential functions are differentiated from first principles. (Mathtutor Video Tutorials) This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
Introduction to differentiation 8.1 - Podcast
Podcast to accompany the Quick Reference Engineering Maths First Aid Kit leaflet 'Introduction to differentiation 8.1' submitted under Creative Commons Licence BY-NC-SA to the mathcentre Community Project by Ciaran Mac an Bhaird, National University of Ireland Maynooth and reviewed by Ann O'Shea, National University of Ireland Maynooth.

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