Question

For x>0 find and simplify the derivative of f(x)= arctan(x) + arctan(1/x).

I've done the problem a few times and I keep getting

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

but something about the answer is wrong and I cannot figure out what.

Answer 1

arctan(1/x) = arccot(x)

f' = 1/(1+x^2) + -1/(1+x^2) = 0

why?

because arccot(x) = pi/2 - arctan(x)

f(x) = pi/2