# How do you find the derivative of e^(1/(2x))?

Use $\frac{d}{\mathrm{dx}} \left({e}^{x}\right) = {e}^{x}$ togerther with the chain rule to see that:
$\frac{d}{\mathrm{dx}} \left({e}^{\frac{1}{2 x}}\right) = {e}^{\frac{1}{2 x}} \cdot \frac{d}{\mathrm{dx}} \left(\frac{1}{2 x}\right)$
$= {e}^{\frac{1}{2 x}} \cdot \left(- \frac{1}{2 {x}^{2}}\right) = - {e}^{\frac{1}{2 x}} / \left(2 {x}^{2}\right)$