If `x^(2)+3x+2,"then "(d^(2)y)/(dx^(2))=` ____________ .

Answer

To find the second derivative \( \frac{d^2y}{dx^2} \) of the function \( y = x^2 + 3x + 2 \), we will follow these steps:

### Step 1: Find the first derivative \( \frac{dy}{dx} \)

We start with the function:
\[ y = x^2 + 3x + 2 \]

To find the first derivative, we differentiate \( y \) with respect to \( x \):
\[ \frac{dy}{dx} = \frac{d}{dx}(x^2) + \frac{d}{dx}(3x) + \frac{d}{dx}(2) \]

Using the power rule for differentiation:
- The derivative of \( x^2 \) is \( 2x \).
- The derivative of \( 3x \) is \( 3 \).
- The derivative of a constant \( 2 \) is \( 0 \).

Thus, we have:
\[ \frac{dy}{dx} = 2x + 3 \]

### Step 2: Find the second derivative \( \frac{d^2y}{dx^2} \)

Now, we differentiate \( \frac{dy}{dx} \) to find the second derivative:
\[ \frac{d^2y}{dx^2} = \frac{d}{dx}(2x + 3) \]

Again, applying the power rule:
- The derivative of \( 2x \) is \( 2 \).
- The derivative of the constant \( 3 \) is \( 0 \).

Thus, we have:
\[ \frac{d^2y}{dx^2} = 2 \]

### Final Answer
Therefore, the second derivative is:
\[ \frac{d^2y}{dx^2} = 2 \]

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