Differentiate the following functions with respect to `x :` `tan^(-1)((a+x)/(1-a x))`

Explanation

Let `tan^(-1)((a+x)/(1-a x))`

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

putting `alpha=tanalpha` and `x=tantheta`

y=`tan^(-1)((tanalpha+tantheta)/(1-tanalpha tantheta))`

=`tan^(-1)tan(alpha-theta)`

=`alpha-theta`

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

`dy/dx=1/(1+x^2)`