aligned & If y= ⁻¹ x 1+ 1-x^2 & + 2 ⁻¹ 1-x 1+x , then d y d x = aligned

Step-by-step solution

Given that, y= ⁻¹ x 1+ 1-x^2 + 2 ⁻¹ 1-x 1+x Let x= 2 aligned & y= ⁻¹ 2 1+ ^2 2 + 2 ⁻¹ 1- 2 1+ 2 & y= ⁻¹ 2 1+ 2 & + 2 ⁻¹ 2 ^2 2 ^2 & y= ⁻¹ ^2 - ^2 ( + )^2 & + 2 ⁻¹( ) & y= ⁻¹ - + + 2 & y= ⁻¹ (1- ) (1+ ) + 2 & aligned aligned & y= ⁻¹ 1- 1+ + 2 & y= ⁻¹ ( ( 4 - ) )+ 2 & y= 4 - + 1- ^2 2 & d y d x = 1 2 1 1-r^2 + 1 2 1-r^2 (2 x) aligned Now, on differentiating w.r.t. x , we get aligned & d y d x = 1 2 1 1-x^2 + 1 2 1-x^2 (-2 x ) & d y d x = 1-2 x 2 1-x^2 aligned