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Integration using a table of anti-derivativesWe may regard integration as the reverse of differentiation. So if we have
a table of derivatives, we can read it backwards as a table of
anti-derivatives. When we do this, we often need to deal with constants
which arise in the process of differentiation.
Product and quotient rulesThis leaflet states and gives examples of the use of the product and quotient rules for differentiation. (Engineering Maths First Aid Kit 8.4
Maxima and MinimaIn this unit we show how differentiation can be used to find the maximum and minimum values of a function. Because the derivative provides information about
the gradient or slope of the graph of a function we can use it to locate points on a
graph where the gradient is zero. We shall see that such points are often associated
with the largest or smallest values of the function, at least in their immediate
locality. In many applications, a scientist, engineer, or economist for example, will
be interested in such points for obvious reasons such as maximising power, or profit, or minimising losses or costs. (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.
Maxima and MinimaIn this unit we show how differentiation can be used to find the maximum and minimum values of a function. Because the derivative provides information about
the gradient or slope of the graph of a function we can use it to locate points on a
graph where the gradient is zero. We shall see that such points are often associated
with the largest or smallest values of the function, at least in their immediate
locality. In many applications, a scientist, engineer, or economist for example, will
be interested in such points for obvious reasons such as maximising power, or profit, or minimising losses or costs. (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.
Differentiating sin(x) and cos(x) from first principlesAfter 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.
Tangents and normalsThis unit explains how to calculate the equation of the tangent and the normal to a curve at a given point.
Integration as a summationThe second major component of the Calculus is called integration. This
may be introduced as a means of finding areas using summation and limits. We
shall adopt this approach in the present Unit. In later units, we shall also
see how integration may be related to differentiation.
Chain Rule examples - Numbas11 questions on the chain rule.
Numbas resources have been made available under a Creative Commons licence by the School of Mathematics & Statistics at Newcastle University.
Product Rule examples - Numbas10 questions on the product rule.
Numbas resources have been made available under a Creative Commons licence by the School of Mathematics & Statistics at Newcastle University.
Quotient Rule examples - Numbas8 questions on the quotient rule.
Numbas resources have been made available under a Creative Commons licence by the School of Mathematics & Statistics at Newcastle University.
Extending the table of derivativesThis unit extends the basic table and produces a more complete and therefore more useful table.
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.
Extending the table of derivativesIn this unit we continue to build up The Table of Derivatives using rules described in other units. (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.
Using a table of derivativesThis unit provides a basic table of some standard derivatives.
Many of the results are derived.
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.
Millenium Bridge - James RobinsonThis 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.
Extending the table of derivativesIn this unit we continue to build up The Table of Derivatives using rules described in other units. (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.
Chain rule practice - Numbas11 Questions on the chain rule. Numbas resources have been made available under a Creative Commons licence by Bill Foster and Christian Perfect, School of Mathematics & Statistics at Newcastle University.
The Chain RuleA special rule, the chain rule, exists for differentiating a function of another function. 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 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.
The Chain RuleThis teach-yourself workbook explains the chain rule which is used to differentiate a function of a function.
