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