Questions: Find the derivative of the function. g(t) = e^(-2 / t^5)

Solution Steps

We start with the function given in the problem: \[ g(t) = e^{-\frac{2}{t^5}} \]

To find the derivative \( g'(t) \), we apply the chain rule. The derivative of the exponential function \( e^u \) is \( e^u \cdot u' \), where \( u = -\frac{2}{t^5} \).

Calculating the derivative of \( u \): \[ u' = \frac{d}{dt}\left(-\frac{2}{t^5}\right) = 10 \cdot t^{-6} = \frac{10}{t^6} \]

Thus, the derivative of \( g(t) \) is: \[ g'(t) = e^{-\frac{2}{t^5}} \cdot \frac{10}{t^6} \]

Combining the results, we have: \[ g'(t) = \frac{10 \cdot e^{-\frac{2}{t^5}}}{t^6} \]

Final Answer