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

##### 1 Answer

#### Explanation:

To solve this, we will be using the quotient rule

and the chain rule

For convenience, let's let

First, we apply the quotient rule to get

We can easily see that

Before moving on, let's let

Then

so, substituting those in,

And now we can substitute back into the original equation to obtain

.

.

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While the above shows a general method, it is worth noting that in this case, we can save some time and effort by observing that

This removes the necessity of using the chain rule, as we can directly calculate the derivative