Optimization of the exponential of the decision variable $x$

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The minima or maxima of optimization problems are typically derived by differentiating the Lagrangean of the objective function w.r.t. the decision variable $x$ being solved for.

Are there any optimization models in any field that contain in their objective function the exponential, $e^{f(x)}$, of the decision variable $x$?

I ask because the first derivative of $e^{x^2}$ for example is $2xe^{x^2}$, meaning the decision variable's presence becomes multiplicitous because of $e$'s chain rule, therefore making it difficult to isolate the decision variable from the Lagrangean first order conditions.

Any examples will do