# What is the equation of the normal line of #f(x)=1/x-lnx/x# at #x=1#?

##### 1 Answer

The normal line has equation

#### Explanation:

Let's start by finding the corresponding

Now, let's differentiate using the power rule, the quotient rule and the identity

We now determine the slope of the tangent by inserting our point into the derivative (since this represents the instantaneous rate of change of the function).

Hence, the slope of the tangent is *perpendicular* to the tangent, so the slope of the normal line is the negative reciprocal of the tangent.

We can now determine the equation of the normal line, because we know the slope

Hopefully this helps!