The derivative of the logarithm

Recall the logarithmic base-change law:

When changing from a base b to base c, for , the logarithm base change formula is defined:

What if we want to find the derivative of any logarithm?

Consider the following example:

We can manipulate this expression in terms of the natural logarithm.

So, chosen base: e

Let's differentiate!

Easy, right?

With this, you've mastered almost everything you need for actually computing derivatives.
Derivatives in Function Analysis - Derivatives of Higher Order

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