If y= ⁻¹ ( 5 x+12 1-x^2 13 ) then d y d x equals

Step-by-step solution

Given y = ⁻¹ ( 5x + 12 1-x^2 13 ) . Let x = , where = ⁻¹ x . Then 1-x^2 = . Substituting these into the expression for y : y = ⁻¹ ( 5 + 12 13 ) Let = 5 13 , which implies = 12 13 . y = ⁻¹ ( + ) y = ⁻¹ ( ( + )) y = + = ⁻¹ x + ⁻¹ ( 5 13 ) Differentiating with respect to x : dy dx = d dx ( ⁻¹ x) + d dx ( ⁻¹ 5 13 ) Since ⁻¹ 5 13 is a constant, its derivative is 0 . dy dx = 1 1-x^2 Answer: 1 1-x^2