If f (x)= x^2-x x^2+2 x then d dx ( f ⁻¹(x) ) at x=2 is

Step-by-step solution

aligned & f (x)=y= x^2-x x^2+2 x = x(x-1) x(x+2) & y= x-1 x+2 & y x+2 y=x-1 2 y+1 1-y =x aligned aligned & f ⁻¹(x)= 2 x+1 1-x & ~d ~d x f ⁻¹(x)= d d x ( 2 x+1 1-x ) &= (1-x)(2)-(2 x+1)(-1) (1-x)^2 &= 2-2 x+2 x+1 (1-x)^2 = 3 (1+x)^2 & ~d dx f ⁻¹(x) at x=2= 3 (1-2)^2 =3 aligned