One of the surprising facts about differentiation is that it is almost always possible to find the expression for the derivative of a function if you have the expression for the function itself. This might not seem surprising until you consider the inverse operation; there are countless examples where having the expression for the derivative doesn't mean that we can find the expression for the function.

This is enormously suggestive of a method by which we can further improve our calculation of derivatives; get the computer to generate the correct expression for us.

This is enormously suggestive of a method by which we can further improve our calculation of derivatives; get the computer to generate the correct expression for us.

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