Differentiation of ⁻¹ ( 1+x^2 -1 x ) w.r.t. ⁻¹ ( 1+ 1+x^2 2 1+x^2 ) , is

Step-by-step solution

Let u = ⁻¹ [ 1+x^2 -1 x ] and v= ⁻¹ [ 1+ 1+x^2 2 1+x^2 ] Put x= , then = ⁻¹ x aligned u & = ⁻¹ [ 1+ ^2 -1 ]- ⁻¹ [ -1 ] & = ⁻¹ [ 1 -1 ]= ⁻¹ [ 1- ] & = ⁻¹ [ 2 ^2 2 2 2 2 ]- ⁻¹ ( 2 )= 2 aligned u = ⁻¹ x 2 aligned v & = ⁻¹ [ 1+ 1+ ^2 2 1+ ^2 ] & = ⁻¹ [ 1+ 2 ] & = ⁻¹ [ 1+ 1 2 ] & = ⁻¹ [ 1+ 2 ] & = ⁻¹ ( 2 ^2 ( 2 ) 2 ) & = ⁻¹ ( 2 )- 0 2 aligned v= ⁻¹ x 2 From (i) and (ii), we get u = v d u d v =1