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The problem asks for the derivative of the function \( y = ax^2 + kx + b \), where \( a \), \( k \), and \( b \) are constants.

To find the derivative, we apply basic differentiation rules:

1. The derivative of \( ax^2 \) with respect to \( x \) is \( 2ax \).
2. The derivative of \( kx \) with respect to \( x \) is \( k \).
3. The derivative of the constant \( b \) with respect to \( x \) is \( 0 \).

Thus, the derivative \( y' \) (or \( \frac{dy}{dx} \)) is:

\[
y' = 2ax + k
\]

Let me know if you need more details or explanations.

### Relative questions:
1. What is the derivative of a cubic function like \( y = bx^3 + ax^2 + kx + c \)?
2. How do you find the second derivative of the function \( y = ax^2 + kx + b \)?
3. What is the physical interpretation of the derivative of a function like this in real-world applications?
4. How does the derivative change if \( b \) is not a constant but a function of \( x \)?
5. What rules are necessary to differentiate more complex functions involving products or quotients of polynomials?

### Tip:
When differentiating polynomials, remember that each term can be treated independently, making it easier to apply the power rule term by term.

Find the derivative of y = ax^2 + kx + b. Assume a, k, and b are constants.

This problem involves finding the derivative of a quadratic function y = ax^2 + kx + b, applying basic differentiation rules such as the power rule. A step-by-step solution is provided. Suitable for students in Grades 11-12.

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