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Derivative of the log of a cubic quantity:

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

We can go a step further and consider it as involving a quantity u:

, where .

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

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

.

Finally, we substitute for u:

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

General Contents

Detailed Contents

Index