Via the Scalar Multiple rule, we can treat this as .

Using the properties of logarithms, this can be written as

We can go a step further and consider each term as involving a quantity u or v:

, where and .

When we eventually apply the Chain Rule, we'll need , and

Combining these partial results and using the derivative of the ln, we get

Finally, we substitute for u and v:

Note that the argument of the denominator in the result is the same as the argument of the logarithm in the original problem.