What is the derivative of ⁻¹ ( 1+x^2 -1 x ) with respect to ⁻¹ x ?

Step-by-step solution

Let y= ⁻¹ [ 1+x^2 -1 x ] and u= ⁻¹ x Put x= = ⁻¹ x Then, y= ⁻¹ [ 1+ ^2 -1 ]= ⁻¹ [ ^2 -1 ] aligned & = ⁻¹ [ -1 ]= ⁻¹ [ 1 -1 ] & = ⁻¹ [ 1- ]= ⁻¹ [ 2 ^2 2 2 2 , 2 ] & 1- =2 ^2 2 and x=2 x 2 x 2 aligned = ⁻¹ [ 2 ] y = 2 y = ⁻¹ x 2 [ = ⁻¹ x ] aligned y & = u 2 dy du & = 1 2 aligned Option (B) is correct.