Differentiate `tan^(-1)((1+a x)/(1-a x))` with respect to `sqrt(1+a^2x^2)dot`

Explanation

`(dU)/(dV)=((dV)/(dx))/((dV)/(dX))`

`U=tan^(-1)((1+ax)/(1-ax))`

`U=tan^(-1)((tanpi/4+ax)/(1-tanpi/4*ax))`

`U=tan^(-1)tanpi/4+tan^(-1)ax`

`(dU)/(dX)=0+a/(1+a^2x^2)`

`V=sqrt(1+a^2x^2)`

`(dV)/(dX)=1/2sqrt(1+a^2x^2)*a^2 2x`

`(dV)/(dU)=a/(1+a^2x^2)*(xsqrt(1+a^2x^2))/(a^2 2x)`

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