If y = (2 ⁻¹ x) then dy dx = ..

Step-by-step solution

Given y = (2 ⁻¹ x) Differentiating with respect to x using the chain rule: dy dx = (2 ⁻¹ x) d dx (2 ⁻¹ x) dy dx = (2 ⁻¹ x) 2 1 - x^2 Using the trigonometric identity (2 ) = 1 - 2 ^2 , we can write: (2 ⁻¹ x) = 1 - 2 ^2( ⁻¹ x) = 1 - 2x^2 Substituting this back into the derivative: dy dx = (1 - 2x^2) 2 1 - x^2 dy dx = 2 - 4x^2 1 - x^2