Chapter 14.3, Problem 80E

If $u=e^{a_1{x}_1+a_2{x}_2+\cdots +a_n{x}_n}$, where $a_1^2+a_2^2+\cdots +a_n^2=1$, show that

$\frac{{\partial }^{2}u}{\partial x_1^2}+\frac{{\partial }^{2}u}{\partial x_2^2}+\cdots +\frac{{\partial }^{2}u}{\partial x_n^2}=u$