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

Explanation

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

### Step 1: Identify the function
We have:
\[ y = (2x + 1)^{-3} \]

### Step 2: Use the chain rule
To differentiate \( y \) with respect to \( x \), we can use the chain rule. We first let:
\[ t = 2x + 1 \]
Thus, we can rewrite \( y \) as:
\[ y = t^{-3} \]

### Step 3: Differentiate \( y \) with respect to \( t \)
Now, we differentiate \( y \) with respect to \( t \):
\[ \frac{dy}{dt} = -3t^{-4} \]

### Step 4: Differentiate \( t \) with respect to \( x \)
Next, we differentiate \( t \) with respect to \( x \):
\[ \frac{dt}{dx} = 2 \]

### Step 5: Apply the chain rule
Now, we can apply the chain rule to find \( \frac{dy}{dx} \):
\[ \frac{dy}{dx} = \frac{dy}{dt} \cdot \frac{dt}{dx} \]
Substituting the derivatives we found:
\[ \frac{dy}{dx} = (-3t^{-4}) \cdot 2 \]

### Step 6: Substitute back for \( t \)
Now, we substitute back \( t = 2x + 1 \):
\[ \frac{dy}{dx} = -6(2x + 1)^{-4} \]

### Final Result
Thus, the differentiation of \( y \) with respect to \( x \) is:
\[ \frac{dy}{dx} = -\frac{6}{(2x + 1)^{4}} \]