If fx=x2−xx2+2x then ddxf−1x=

y=fx=xx−1xx+2=x−1x+2  if  x≠0Cross multiply and then simplify⇒xy+2y=x−1⇒x1−y=2y+1⇒x=2y+11−y⇒f−1y=2y+11−y⇒f−1x=2x+11−x.Differentiate both sides with  respect to xddxf−1x=1−x2−2x+1−11−x2=2−2x+2x+11−x2=31−x2