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**HallsofIvy** By the way, for distance functions generally, that is $\displaystyle \sqrt{(x-a)^2+ (y-b)^2}$, perhaps with other conditions, "minimizing" the distance is exactly the same as minimzing the **square** of the distance. So, instead of taking the derivative of $\displaystyle \sqrt{x^2 + e^{2x}}$, you could have just minimized $\displaystyle x^2+ e^{2x}$. Then, instead of setting $\displaystyle \frac{2x + 2e^{2x}}{2\sqrt{x^2+e^{2x}}}= 0$ you would have just $\displaystyle 2x+ 2e^{2x}= 0$. Of course, that what you get anyway after multiplying through by the denominator but the derivative is a little easier.