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Repeated Differentiation I am going to investigate what effect differentiation has on several different functions of x and try to find general rules for the nth differential for each function. I'm interested in investigating this particular topic as I enjoy differentiation and integration in the A-Level class work I do and would like to take it further to see I can find any patterns and hopefully find general formulae for nth differentials. Repeated differentiation to A-Level standard is really only used up to the second differential of a function, as this gives the turning points on the graph of the function. In this piece of coursework I will look into what happens when functions are differentiated n times and the results achieved when different functions are multiplied together. I am going to first study repeated differentiation on a simple function of x, for example a.xb , and then look at increasingly more complicated...

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