Section 14.3 Partial Derivatives

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