How do you differentiate ln(x)?

When it comes to working with natural logarithms and combining it with differentiation, this can cause a number of errors to be made. 

You will generally be shown the proof or your textbook will have it. But once you have seen the result, it is generally used as a standard result for further questions. 

The standard result is as follows: 

If y = \ln(x), then: 

So what is this telling us if anything?

It is telling us the slope of lnx gets smaller and smaller as x

It is important to remember then this simply means that the rate of change decreases as x increases. gets bigger and bigger. The slope will get closer and closer to 0, but never actually reaches it. 

Classroom insight

Do not treat ln(x) as another power function. Its derivative is very different. Understand the graph and be ready to know when to use the standard result.