If y= ax ^ n +1 + b x^ - n , then x^2 ~d ^2 y ~d x^2 =

Step-by-step solution

y=a x^ n +1 + b x^ - n Differentiating w.r.t. x , we get aligned & d y ~d x = a ( n +1) x^ n +1-1 + b (- n ) x^ - n -1 & ~d y ~d x = a ( n +1) x^ n - bn x^ - n -1 aligned Again differentiating w.r.t. x , we get aligned d ^2 y ~d x^2 & =a(n+1)^n x^ n -1 -b n(-n-1) x^ -n-1-1 & =a(n+1) n x^ n-1 +b n(n+1) x^ -n-2 & =n(n+1) a x^n x +n(n+1) b x^ -n x^2 aligned array ll & d ^2 y ~d x^2 = n ( n +1) x^2 [ a x^ n +1 + b x^ - n ] & x^2 ~d ^2 y ~d x^2 = n ( n +1) y array