Evaluate differentiation of y with respect to x:
`((1)/(3x-2))`

Explanation

To evaluate the differentiation of \( y \) with respect to \( x \) for the function \( y = \frac{1}{3x - 2} \), we can follow these steps:

### Step 1: Define the function
We start with the function:
\[ y = \frac{1}{3x - 2} \]

### Step 2: Use substitution
To simplify the differentiation process, we can introduce a substitution. Let:
\[ t = 3x - 2 \]
Thus, we can rewrite \( y \) in terms of \( t \):
\[ y = \frac{1}{t} \]

### Step 3: Differentiate using the chain rule
We want to find \( \frac{dy}{dx} \). By using the chain rule, we can express this as:
\[ \frac{dy}{dx} = \frac{dy}{dt} \cdot \frac{dt}{dx} \]

### Step 4: Differentiate \( y \) with respect to \( t \)
Now, we differentiate \( y \) with respect to \( t \):
\[ \frac{dy}{dt} = \frac{d}{dt}\left(t^{-1}\right) = -t^{-2} = -\frac{1}{t^2} \]

### Step 5: Differentiate \( t \) with respect to \( x \)
Next, we differentiate \( t \) with respect to \( x \):
\[ \frac{dt}{dx} = \frac{d}{dx}(3x - 2) = 3 \]

### Step 6: Combine the results
Now, we can substitute back into our chain rule expression:
\[ \frac{dy}{dx} = \left(-\frac{1}{t^2}\right) \cdot 3 = -\frac{3}{t^2} \]

### Step 7: Substitute \( t \) back
Finally, substitute \( t = 3x - 2 \) back into the expression:
\[ \frac{dy}{dx} = -\frac{3}{(3x - 2)^2} \]

### Final Answer
Thus, the differentiation of \( y \) with respect to \( x \) is:
\[ \frac{dy}{dx} = -\frac{3}{(3x - 2)^2} \]

---