# How do you find the derivative of #(1+x)^(1/x)#?

##### 1 Answer

Feb 5, 2017

#### Explanation:

Consider:

The function is defined only for

and using the properties of logarithms:

Now differentiate both sides, using the chain rule at first member and the product rule at the second member:

and since we know

Alternatively we can write the function as:

using the chain rule:

which is the same expression we had in the other way.