Derivative of ⁻¹ ( 1+x^2 - 1-x^2 1+x^2 + 1-x^2 ) w.r.t. ⁻¹ x^2 is

Step-by-step solution

Let y= ⁻¹ ( 1+x^2 - 1-x^2 1+x^2 + 1-x^2 ) and z = ⁻¹ (x^2 ) Put x^2= 2 = 1 2 ⁻¹ x^2 aligned y & = ⁻¹ ( 1+ 2 - 1- 2 1+ 2 + 1- 2 ) y & = ⁻¹ ( - + ) y & = ⁻¹ ( 1- 1+ ) y & = ⁻¹ ( ( 4 - ) ) y & = 4 - 1 2 ⁻¹ x^2 y & = 4 - 1 2 z dy dz & =- 1 2 aligned