The derivative of (y= ⁻¹ [ 1+ x + 1- x 1+ x - 1- x ] with ) respect to (x ) is equal to

Step-by-step solution

It is given that, ( aligned & y= ⁻¹ [ 1+ x + 1- x 1+ x - 1- x ] & 1+ x = ^2 x 2 + ^2 x 2 +2 x 2 x 2 & = | x 2 + x / 2 | aligned ) and ( 1- x = ^2 x 2 + ^2 x 2 -2 x 2 x 2 ) (= | x 2 - x 2 | ) ( y= ⁻¹ ( x 2 ) ) when ( x 2 + x 2 ) and ( x 2 - x 2 = 2 - x 2 ) are positive ( ⁻¹ ( x 2 )= x 2 ), when ( x 2 + x 2 ) is positive and ( x 2 - x 2 ) is negative ( ⁻¹ ( x 2 )= x 2 ), when ( x 2 + x 2 ) is negative and ( x 2 - x 2 ) is positive ( ⁻¹ ( x 2 )= 2 - x 2 ), when ( x 2 + x 2 ) and as ( x 2 - x 2 ) is negative. So, ( d y