To differentiate the expression \(2x^2 + 3x + 4\) with respect to \(x\), we will follow these steps:
1. **Identify the function**: Let \(y = 2x^2 + 3x + 4\).
2. **Differentiate each term**: We will differentiate each term of the function separately.
- For the first term \(2x^2\):
- Use the power rule: \(\frac{d}{dx}(x^n) = n \cdot x^{n-1}\).
- Here, \(n = 2\), so the derivative is \(2 \cdot 2x^{2-1} = 4x\).
- For the second term \(3x\):
- Again, using the power rule, where \(n = 1\), the derivative is \(3 \cdot 1 \cdot x^{1-1} = 3\).
- For the third term \(4\):
- The derivative of a constant is \(0\).
3. **Combine the derivatives**: Now, we can combine the results from the differentiation of each term:
\[
\frac{dy}{dx} = 4x + 3 + 0 = 4x + 3.
\]
4. **Final result**: Therefore, the differentiation of \(2x^2 + 3x + 4\) with respect to \(x\) is:
\[
\frac{dy}{dx} = 4x + 3.
\]
### Summary of the Solution:
The differentiation of \(2x^2 + 3x + 4\) with respect to \(x\) is \(4x + 3\).
To differentiate the expression \(2x^2 + 3x + 4\) with respect to \(x\), we will follow these steps:
1. **Identify the function**: Let \(y = 2x^2 + 3x + 4\).
2. **Differentiate each term**: We will differentiate each term of the function separately.
- For the first term \(2x^2\):
- Use the power rule: \(\frac{d}{dx}(x^n) = n \cdot x^{n-1}\).
...
