We can use the chain rule to differentiate the expression (e^u)(du/dx):
d/dx[e^u·(du/dx)] = e^u·(d/du[du/dx])·(du/dx)
Simplifying,
d/dx[e^u·(du/dx)] = e^u·d^2u/dx^2
Therefore, the derivative of (e^u)(du/dx) with respect to x is e^u times the second derivative of u with respect to x (i.e. d^2u/dx^2).
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