In this screen capture video we show how the derivatives of the exponential function (e^x) and natural logarithm follow from the definitions of the derivative and of the number e.  [Released under Creative Commons Attribution-NonCommercial-ShareAlike 2.0 UK: England &amp; Wales licence.]

Derivative of exponential and logarithmic functions from first principles

These resources are produced at Plymouth University to support the understanding of mathematics and its importance in many careers. Mathematics and Statistics at Plymouth University has a long tradition in teaching and research. We are very proud of the support that we offer our students and the facilities available to them. Our graduates have excellent career opportunities.

This video quiz contains three questions on Maclaurin series followed by answers and, then, detailed solutions. Two of the questions contain ways to check your answer.  [Released under Creative Commons Attribution-NonCommercial-ShareAlike 2.0 UK: England &amp; Wales licence.]

Maclaurin series quiz

This screen capture video contains integrals for you to calculate using trigonometric changes of variables. Full solutions are provided.  [Released under Creative Commons Attribution-NonCommercial-ShareAlike 2.0 UK: England &amp; Wales licence.]

Trigonometric change of variable quiz

This screen capture video contains integrals for you to calculate using partial fraction decompositions of the integrands. Full solutions are provided.  [Released under Creative Commons Attribution-NonCommercial-ShareAlike 2.0 UK: England &amp; Wales licence.]

Partial fraction integral quiz

This screen capture video discusses the notation and interpretation of multiple integration. A simple example of a double integral is calculated to demonstrate the geometric interpretation of such integrals.   [Released under Creative Commons Attribution-NonCommercial-ShareAlike 2.0 UK: England &amp; Wales licence.]

Multiple integrals

This screen contains two worked examples of the calculation of multiple (double) integrals.In one the order of integration is changed.  [Released under Creative Commons Attribution-NonCommercial-ShareAlike 2.0 UK: England &amp; Wales licence.]

Derivative of exponential and logarithmic functions from first principles

Download our free app to listen on your phone