If y= ⁻¹ x ²-1 , then the ratio d ² y dx x ² : dy dx is

Step-by-step solution

y = ⁻¹ x ²-1 , Put array l x = dx = d array . y = ⁻¹ ² -1 = ⁻¹( )= = ⁻¹ x dy dx = d dx ( ⁻¹ x )= 1 x x ²-1 aligned d ² y dx &= 1 x -1 2 1 ( x ²-1 )^ 3 / 2 (2 x )- 1 x ² 1 x ²-1 =- 1 ( x ²-1 )^ 3 / 2 - 1 x ² ( x ²-1 )^ 1 / 2 =- 1 x ² ( x ²-1 )^ 3 / 2 ( x ²+ x ²-1 ) =- (2 x ²-1 ) x ² ( x ²-1 )^ 3 / 2 aligned aligned & Now, d² y d x² : d y d x =- (2 x²-1 ) x² (x²-1 )^ 3 / 2 : 1 x (x²-1 )^ 1 / 2 & d² y d x² : d y d x = (1-2 x² ): x (x²-1 ) & or ( d² y d x² d y )= (1-2 x² ) x (x²-1 ) aligned