You can use the chain rule:
d f(g(x)) / d x = d f(g(x)) / d g(x) + d g(x) / d x
Applying it to our problem:
d e^(g(x)) / d x = d e^(g(x)) / d g(x) + d g(x) / d x = e^(g(x)) + g'(x)
Now we only have to solve the derivative for g(x)
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