Is Cot-1x the Same as 1/Tan-1x?

[Jules18]

My notes say the deriv. of inverse Cotangent is -1/(1+x²)

But when I plot the derivative of this function: 1/Tan^-1x
against -1/(1+x²), I get two different graphs.

Is Cot^-1x not the same thing as 1/Tan^-1x ?

~Jules~

 

[Bohrok]

They are not the same.

Let y = cot^-1x
cot y = x
1/coty = tan y = 1/x
y = tan^-1(1/x)

cot^-1x = tan^-1(1/x)

 

[Jules18]

thanks