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What is the derivative of #cot^-1(x)#?

1 Answer

Jun 9, 2018

#dy/dx=-1/(x^2+1)#

Explanation:

Let #y=arccot(x)#
then
#cot(y)=x#
so

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

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

#dy/dx=-1/(1+x^2)#
since #cot(y)=x#

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