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I see that you've uploaded an image with some mathematical content. Let me analyze it to provide you with a solution.The image contains the following mathematical expression:

\[
\frac{d}{dx}\left( e^{3x} \right)
\]

This is the derivative of the exponential function \( e^{3x} \) with respect to \( x \).

### Solution:

We can apply the chain rule for this derivative. The derivative of \( e^{u} \) with respect to \( u \) is \( e^{u} \), and we multiply by the derivative of the inner function (in this case, \( 3x \)).

\[
\frac{d}{dx} \left( e^{3x} \right) = e^{3x} \cdot \frac{d}{dx}(3x)
\]

Since \( \frac{d}{dx}(3x) = 3 \), we have:

\[
\frac{d}{dx} \left( e^{3x} \right) = 3e^{3x}
\]

Thus, the derivative is:

\[
\boxed{3e^{3x}}
\]

Would you like more details or clarifications? Here are some related questions you might find interesting:

1. How would you differentiate \( e^{kx} \) where \( k \) is a constant?
2. What is the chain rule and how does it apply to composite functions?
3. How do we differentiate functions that include trigonometric terms, like \( e^{x} \sin(x) \)?
4. What is the general formula for the derivative of an exponential function with a constant multiplier?
5. How can we apply the product rule to differentiate \( x e^{3x} \)?

**Tip**: Whenever differentiating an exponential function, always remember to check for an inner function that requires the chain rule!

This solution explains how to differentiate the exponential function e^{3x} using the chain rule. Step-by-step, it demonstrates applying the rule to solve for the derivative and discusses the key concepts involved. Suitable for students in Grades 11-12.

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