# What is the derivative of #ln(1+1/x) / (1/x)#?

##### 2 Answers

I like the form:

#### Explanation:

Before we differentiate, let's get rid of that silly "divided by

We can now use the product rule, but also note that

So we have

When we differentiate the second factor, we'll need the chain rule and we'll need

So, here we go:

# = [1] ln((x+1)/x) + x[1/((x+1)/x) ((-1)/x^2)]#

# = ln((x+1)/x)+ x^2/(x+1)((-1)/x^2)#

# = ln((x+1)/x)-1/(x+1)#

Nov 22, 2015

Using the **property of logs** ...

#### Explanation:

Using only the **product rule** :

Now simplify ...

hope that helped