Differentiate the following w.r.t. x :
`3x(2x-1) (x+2)`

Answer

To differentiate the expression \(3x(2x-1)(x+2)\) with respect to \(x\), we will follow these steps:

### Step 1: Expand the expression
First, we need to expand the expression \(3x(2x-1)(x+2)\).

\[ 3x(2x-1)(x+2) = 3x[(2x-1)(x+2)] \]

Now, let's expand \((2x-1)(x+2)\):

\[ (2x-1)(x+2) = 2x^2 + 4x - x - 2 = 2x^2 + 3x - 2 \]

Now, substituting back into the expression:

\[ 3x(2x^2 + 3x - 2) = 6x^3 + 9x^2 - 6x \]

### Step 2: Differentiate the expanded expression
Now we differentiate \(6x^3 + 9x^2 - 6x\) with respect to \(x\).

Using the power rule \( \frac{d}{dx}(x^n) = nx^{n-1} \):

\[ \frac{d}{dx}(6x^3) = 18x^2 \]
\[ \frac{d}{dx}(9x^2) = 18x \]
\[ \frac{d}{dx}(-6x) = -6 \]

Combining these results, we get:

\[ \frac{d}{dx}(6x^3 + 9x^2 - 6x) = 18x^2 + 18x - 6 \]

### Final Answer
Thus, the derivative of the expression \(3x(2x-1)(x+2)\) with respect to \(x\) is:

\[ \boxed{18x^2 + 18x - 6} \]