If y = ^2 [ ⁻¹ ( 1 - x 1 + x ) ] then dy dx = ........

Step-by-step solution

Let x = . Substituting this in the given expression: 1 - x 1 + x = 1 - 1 + = 2 ^2( /2) 2 ^2( /2) = ( 2 ) The expression for y becomes: y = ^2 [ ⁻¹ ( ( 2 ) ) ] Using the identity ( 2 ) = ( 2 - 2 ) : y = ^2 [ ⁻¹ ( ( 2 - 2 ) ) ] y = ^2 ( 2 - 2 ) y = ^2 ( 2 ) Using the half-angle formula ^2 ( 2 ) = 1 - 2 : y = 1 - x 2 Differentiating with respect to x : dy dx = d dx ( 1 2 - x 2 ) = - 1 2 Answer: -1 2