The given function is:

$y = 9t^2 + 2e^t$

To find the derivative $y'$, we will differentiate each term of the function with respect to $t$.

1. The derivative of $9t^2$ is $18t$, using the power rule: $\frac{d}{dt}(t^n) = nt^{n-1}$.
2. The derivative of $2e^t$ is $2e^t$, because $e^t$ remains $e^t$ when differentiated.

Thus, the derivative $y'$ is:

$y' = 18t + 2e^t$

Would you like a further breakdown or details on this solution?

Here are 5 related questions to further your understanding:

1. What is the derivative of $e^{kt}$ for any constant $k$?
2. How do you apply the power rule when differentiating a function like $t^n$?
3. Can you differentiate $y = t^2 \sin(t) + 3e^t$?
4. How would you find the second derivative of $y = 9t^2 + 2e^t$?
5. What is the derivative of a product of functions, like $t^2 e^t$?

Tip: Always apply the power rule and chain rule carefully when differentiating complex functions involving powers and exponentials.