# What is the derivative of # y=cot (arctan x) #?

##### 1 Answer

Sep 13, 2017

# d/dx cot (arctan x) = -1/x^2 #

#### Explanation:

We have:

# y=cot (arctan x) #

Suppose we let:

# tanu = x <=> u = arctan x#

Then:

# cot u = 1/(tan u) = 1/x #

But, we established that

# cot (arctan x) = 1/x #

Hence, we have:

# y = 1/x => dy/dx = -1/x^2 #