The second order derivative of ⁻¹(4x^3 - 3x) with respect to ⁻¹(2x^2 - 1) , where 1 2 < x < 1 is

Step-by-step solution

Let u = ⁻¹(4x^3 - 3x) and v = ⁻¹(2x^2 - 1) . Substitute x = . Since 1 2 For u : u = ⁻¹(4 ^3 - 3 ) = ⁻¹( 3 ) Since 0 Thus, u = 3 . For v : v = ⁻¹(2 ^2 - 1) = ⁻¹( 2 ) Since 0 Thus, v = 2 . We can express u in terms of v as: u = 3 2 v Differentiating u with respect to v , we get the first order derivative: du dv = 3 2 Differentiating again with respect to v , we get the second order derivative: d^2u dv^2 = d dv ( 3 2 ) = 0 Answer: 0