If y=[x+√x2+a2]n,then dydx is equal to
ny√x2+a2
−ny√x2+a2
nx√x2+a2
−nx√x2+a2
Using chain rule, we have dydx=ddx[{x+√x2+a2}n] =n{x+{√x2+a2}}n−1.ddx{x+√x2+a2} =n{x+√x2+a2}n−1{√x2+a2+x√x2+a2} =n{x+√x2+a2}n√x2+a2=ny√x2+a2