Let y = tan-1ax-bbx+a=tan-1aa×x-ba1+bax=tan-1x-ba1+bax=tan-1x-tan-1baNow differentiating wrt x we get, dydx=11+x2-0=11+x2

Prove for dy/dx

Let y = \tan^{- 1} (\frac{ax - b}{bx + a}) = \tan^{- 1} (\frac{a}{a} \times \frac{x - \frac{b}{a}}{1 + \frac{b}{a} x}) = \tan^{- 1} (\frac{x - \frac{b}{a}}{1 + \frac{b}{a} x}) = \tan^{- 1} x - \tan^{- 1} \frac{b}{a} Now differentiating wrt x we get, \frac{dy}{dx} = \frac{1}{1 + {(x)}^{2}} - 0 = \frac{1}{1 + x^{2}}