Quotient rule, for differentiation

For functions involving a combination of other elementary functions, we follow another set of rules if u and v represent functions fix) and g(x), respectively, then the rules for differentiating a sum, product or quotient can be expressed as  

To differentiate AG/T, apply the rule for differentiating a quotient to give 

Let us now differentiate AG/T, with respect to temperature. From the usual rule for differentiating a quotient, we find that  

The partial derivative with respect to V is somewhat trickier. For the first term we use the rule for differentiating a quotient (Chapter 35) while for the second we write l/V as The partial derivative is thus 

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. 

---