Match the differentials from column I with their domains of column II

A. We know that 2tan−1⁡x=sin−1⁡2x1+x2, if −1≤x≤1π−sin−1⁡2x1+x2, if x>1−π−sin−1⁡2x1+x2, if x<−1⇒dydx=−21+x2 if x<−1 or x>1 B. cos−1⁡11+x2=tan−1⁡x, x≥0−tan−1⁡x,x<0⇒dydx=−11+x2 if x<0C.y=e|x|−e=ex−e,x≥0e−x−e,x<0=ex−e,x≥1e−ex,0≤x<1e−e−x,−1≤x<0e−x−e,x<−1⇒dydx>0 if x>1 or −10−11+x2,x<0⇒dudv=1+x2x,x>0−1+x2x,x<0 Now we know that 1+x2x=x+1x>2 if x>1 and <−2 if x<−1⇒dudv>2 if x<−1 or x>1