Questions: Differentiate the function y=e^(0.8 t). dy/dt=

Transcript text: Differentiate the function $y=e^{0.8 t}$. \[ \frac{d y}{d t}= \]

Solution

Solution Steps

Step 1: Define the Function

We start with the function given by \[ y = e^{0.8t}. \]

Step 2: Differentiate the Function

To find the derivative of $y$ with respect to $t$, we apply the rule for differentiating exponential functions. The derivative of $e^{ax}$ is $ae^{ax}$, where $a$ is a constant. Here, $a = 0.8$. Thus, we have: \[ \frac{dy}{dt} = 0.8 e^{0.8t}. \]

Final Answer

The derivative of the function is \[ \boxed{\frac{dy}{dt} = 0.8 e^{0.8t}}. \]

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