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