# What is the derivative of #y=cot^{-1}(x)#?

##### 1 Answer

Sep 14, 2014

The answer is

We start by using implicit differentiation:

#y=cot^(-1)x#

#cot y=x#

#-csc^2y (dy)/(dx)=1#

#(dy)/(dx)=-1/(csc^2y)#

#(dy)/(dx)=-1/(1+cot^2y)# using trig identity:#1+cot^2 theta=csc^2 theta#

#(dy)/(dx)=-1/(1+x^2)# using line 2:#cot y = x#

The trick for this derivative is to use an identity that allows you to substitute