Questions: Find the derivative of f(t) = e^(t+3)

Solution Steps

To find the derivative of the function \( f(t) = e^{t+3} \), we can use the chain rule. The chain rule states that the derivative of \( e^{u} \) with respect to \( t \) is \( e^{u} \cdot \frac{du}{dt} \). Here, \( u = t + 3 \), so we need to find the derivative of \( u \) with respect to \( t \), which is 1.

We start with the function given by \( f(t) = e^{t + 3} \).

To find the derivative \( f'(t) \), we apply the chain rule. The derivative of \( e^{u} \) with respect to \( t \) is given by: \[ f'(t) = e^{u} \cdot \frac{du}{dt} \] where \( u = t + 3 \). The derivative of \( u \) with respect to \( t \) is: \[ \frac{du}{dt} = 1 \]

Substituting back into the derivative formula, we have: \[ f'(t) = e^{t + 3} \cdot 1 = e^{t + 3} \]

Final Answer