If r =a e^ where a and are real numbers, then d² r d ² -4 r ² is

Step-by-step solution

Given, r =a e^ Differentiating w.r.t. , aligned 1 2 r d r d &=a e^ d r d &=2 a r e^ d r d &=2 a a e^ e^ aligned [from Eq. (i)] d r d =2 a² e^ 2000 t Again r differentiating w.r.t. d² r d ² =2 a² e^ 2 2 d² r d ² =4 a² ² e^ 20 d² r d ² =4 ² (a e^ )² d² r d ² =4 ² ( r )² [from Eq. (i)] d² r d ² -4 r ² =0