Find the derivative of the function. \[ y=e^{-4 / x} \]

1. Let \( u = -\frac{4}{x} \) so that \( y = e^u \). 2. Differentiate \( u \) with respect to \( x \): \[ \frac{du}{dx} = \frac{d}{dx}\left(-\frac{4}{x}\right) = -4 \cdot \frac{d}{dx}\left(\frac{1}{x}\right) = -4 \cdot \left(-\frac{1}{x^2}\right) = \frac{4}{x^2}. \] 3. Apply the chain rule for differentiation, which gives: \[ \frac{dy}{dx} = e^u \cdot \frac{du}{dx}. \] 4. Substitute back for \( u \): \[ \frac{dy}{dx} = e^{-4/x} \cdot \frac{4}{x^2}. \] The derivative of the function is: \[ \frac{dy}{dx} = \frac{4e^{-4/x}}{x^2}. \]