Differentiating Combinations of Functions

Problems in chemistry sometimes require the differentiation of functions which are more complicated than those discussed so far. In the previous chapter it was seen how to differentiate a function multiplied by a constant, and sums and differences of simple functions. For completeness, these rules are formalised here, before products and quotients of functions are considered. 

If the function f x) is multiplied by a constant a to form the product a/(x), its derivative is given by 

As seen previously, sums and differences of functions are differentiated term by term. Thus to differentiate the sum f x) + g x we have 

Similarly, to differentiate the difference of these functions /(x) (x), we have 

This is best remembered in words as differentiate first, multiply by second, plus differentiate second, multiply by first . For example. 

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