If y= 1- ⁻¹(x) 1+ ⁻¹(x) , then d y ~d x at x=0 and y=1 is

Step-by-step solution

y= 1- ⁻¹(x) 1+ ⁻¹(x) Taking log on both sides, we get y= 1 2 [ (1- ⁻¹ x )- (1+ ⁻¹ x ) ] Differentiating w. r. t. x , we get aligned & 1 y d y ~d x = 1 2 [ 1 1- ⁻¹ x -1 1-x^2 - 1 1+ ⁻¹ x 1 1-x^2 ] & d y ~d x = -y 2 1-x^2 ( 1 1- ⁻¹ x + 1 1+ ⁻¹ x ) & ( d y ~d x )_ (0,1) = 1 2(1) ( 1 1-0 + 1 1+0 )=-1 aligned