Using the chain rule of differentiation, we have:
d/dx(e^u) = d/dx(e^(u(x))) = d/du(e^u) * du/dx
Since u is a function of x, we need to apply the chain rule to evaluate du/dx:
du/dx = d/dx(u(x))
Putting this all together, we get:
d/dx(e^u) = d/du(e^u) * d/dx(u(x)) = e^u * du/dx
Therefore, the derivative of e^u with respect to x is e^u times the derivative of u with respect to x.
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