If f(x)= ⁻¹ ( x^x-x^ -x 2 ) , then f^ (1)=

Step-by-step solution

Given, gathered f(x)= ⁻¹ ( x^x-x^ -x 2 ) y= ⁻¹ ( x^ 2 x -1 2 x^x ) gathered Put x^x= aligned y & = ⁻¹ ( ^2 -1 2 ) & = ⁻¹(- 2 ) y & = - ⁻¹( 2 ) y & = -2 y & = -2 ⁻¹ (x^x ) d y d x & =- 2 1+x^ 2 x x^x(1+ x) aligned So, . d y d x |_ x=1 = -2 1+(1)^2 1^1(1+ 1) =- 2 2 1=-1