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=e0.8t.
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 eax is aeax, where a is a constant. Here, a=0.8. Thus, we have:
dtdy=0.8e0.8t.
Final Answer
The derivative of the function is
dtdy=0.8e0.8t.