Find the derivative of the function:
![\[ f(x) = e^{\frac{1}{x}}. \]](https://www.stumblingrobot.com/wp-content/ql-cache/quicklatex.com-726314a34eda28073402d40bf57e7fe2_l3.png "Rendered by QuickLaTeX.com")
Using the formula for the derivative of the exponential and the chain rule we compute,
![\[ f'(x) = \left( \frac{-1}{x^2} \right) e^{\frac{1}{x}} = -\frac{e^{\frac{1}{x}}}{x^2}. \]](https://www.stumblingrobot.com/wp-content/ql-cache/quicklatex.com-0a18229b6785ae03e54cbd91710e8dfa_l3.png "Rendered by QuickLaTeX.com")
Find the derivative of the function:
Using the formula for the derivative of the exponential and the chain rule we compute,