# What is the derivative of arctan(x)+arctan(1/x)?

##### 1 Answer

#### Explanation:

Alternatively, we can simplify the original function.

#y=arctan(x)+arctan(1/x)#

Take the tangent of both sides.

#tan(y)=tan(arctan(x)+arctan(1/x))#

Use the tangent addition formula:

Here, for

#tan(y)=(tan(arctan(x))+tan(arctan(1/x)))/(1-tan(arctan(x))tan(arctan(1/x))#

#tan(y)=(x+1/x)/(1-x(1/x))#

#tan(y)=((x^2+1)/x)/(1-1)#

#tan(y)=(x^2+1)/0#

This is an undefined value: however, we know that the tangent of

So, we know that

#y=pi/2" "# or#" "y=-pi/2#

Thus,

#arctan(x)+arctan(1/x)=+-pi/2#

And the derivative of