Differentiate the following functions with respect to `x` : `tan^(-1)((a+x)/(1-a x))` (ii) `tan^(-1)((acosx-bsinx)/(bcosx+asinx)),\ -pi/2-1`

Answer

N/a

Explanation

Let ` y = tan^(-1)((acosx-bsinx)/(bcosx+asinx))`
`=tan^(-1)[((acosx)/(bcosx)-(bsinx)/(bcosx))/((bcosx)/(bcosx)+(asinx)/(bcosx))]= tan^(-1)[((a)/(b)-tanx)/(1+(a)/(b)tanx)]`
`=tan^(-1)'(a)/(b)-tan^(-1)tanx, [:'tan^(-1)x-tan^(-1)y=tan^(-1)((x-y)/(1+xy))]`
`=tan^(-1)'(a)/(b)-x`
`:. (dy)/(dx)=(d)/(dx)(tan^(-)'a/b)-d/dx(x)`
`=0-1, [:'(d)/(dx)(a/b)=0]`
`= -1`