From the image you've provided, the problem is asking to find $\frac{dy}{dx}$ where:

$y = (3x - 2)^3$

You have already begun solving this by introducing $u = 3x - 2$, making the expression $y = u^3$. Here's how to complete the process step by step:

Step-by-step solution:

1. Substitute $y$ in terms of $u$: $y = u^3$

2. Differentiate $y = u^3$ with respect to $u$: $\frac{dy}{du} = 3u^2$

3. Differentiate $u = 3x - 2$ with respect to $x$: $\frac{du}{dx} = 3$

4. Chain Rule: Using the chain rule, $\frac{dy}{dx} = \frac{dy}{du} \times \frac{du}{dx}$: $\frac{dy}{dx} = 3u^2 \times 3 = 9u^2$

5. Substitute back $u = 3x - 2$: $\frac{dy}{dx} = 9(3x - 2)^2$

So, the derivative is:

$\frac{dy}{dx} = 9(3x - 2)^2$

Would you like more details on any of these steps, or do you have any questions?

Related questions:

1. How do you apply the chain rule in more complex expressions?
2. Can you explain implicit differentiation and when to use it?
3. How do derivatives of higher-order polynomials differ from simple ones?
4. How do you find the second derivative $\frac{d^2y}{dx^2}$ for this function?
5. What are some practical applications of this type of derivative?

Tip:

When using the chain rule, always check for inner functions that can be substituted to simplify the differentiation process!