Question #7b4a1

1 Answer
John D.
Jun 5, 2017

#(x^2-1)/(x^2+(x^2+1)^2)#

Explanation:

First, recall the formula:

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

We will need chain rule for our derivative:

#d/dx(tan^-1(x+1/x))#

#= d/(d(x+1/x))(tan^-1(x+1/x)) xx d/dx(x+1/x)#

#= 1/(1+(x+1/x)^2)times(1-1/x^2)#

#=1/(1+x^2+2+1/x^2) xx ((x^2-1)/x^2)#

#= (x^2-1)/(x^2+x^4+2x^2+1)#

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

Final Answer

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