d d x ( ⁻¹ ( x- 1 x x+ 1 x ) )=

Step-by-step solution

Let y= ⁻¹ ( x- 1 x x+ 1 x ) aligned & = ⁻¹ ( x^2-1 x^2+1 )= ⁻¹ [(-1) ( 1-x^2 1+x^2 ) ] y= & - ⁻¹ ( 1-x^2 1+x^2 ) aligned array ll & Put x= & = ⁻¹ x & y= - ⁻¹ ( 1- ^2 1+ ^2 ) & y= - ⁻¹( 2 ) & y= -2 & y= -2 ⁻¹ x array Differentiating w.r.to x , we get d y ~d x =0- 2 1+x^2 = -2 1+x^2