Differentiate the following function with respect to `x :` `tan^(-1)((a+btanx)/(b-atanx))`

Explanation

Let `y = tan^-1((a+btanx)/(b - a tanx))`

`=>y = tan^-1((a/b+tanx)/(1 - a/b tanx))`....[Dividing numerator and denominator by `b`]

Now, `tan^-1((m+n)/(1-mn)) = tan^-1m+tan^-1n`

`:. y = tan^-1(a/b) + tan^-1(tanx)`

`=> y = tan^-1(a/b) + x`

Now, Differentiating both sides w.r.t. `x`,

`=>dy/dx = 0+1`

`=>dy/dx = 1`