Derivative of the ln of a quadratic 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.
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