# How do you find the derivative of #f(x) = ln (3x^2 - 1)#?

##### 1 Answer

Jun 21, 2016

#### Explanation:

There is a rule for differentiating natural logarithm functions:

If

#f(x)=ln(g(x))# , then#f'(x)=(g'(x))/g(x)# .

This can be derived using the chain rule:

Since

#d/dxln(x)=1/x# , we see that#d/dxln(g(x))=1/(g(x))*g'(x)=(g'(x))/g(x)# .

So, when we have

Thus,

#f'(x)=(g'(x))/g(x)=(6x)/(3x^2-1)#