Answer to Question #124123 in Calculus for Desmond

Question

Find the derrivative of
f(x) = tan⁻¹((1-x)/(1+x))

Answer 1

X=tanθ

Y=tan^-1((1-tanθ )/(1+tanθ))

=tan^-1((tan(π /4)-tan θ )/(1+tan( $\pi$  /4)tanθ ))

=tan^-1(tan($\pi$/4-θ))

=$\pi$ /4-θ,

Formula (tan(π /4))=1,

dy/dx=d/dx($\pi$ /4-tan^-1x)

Answer: dy/dx=-1/(1+x²)