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The problem asks for the derivative of the function \( y = 3x^2 + 5x + 6 \).

To solve this, we can use basic differentiation rules:

1. The derivative of \( x^n \) is \( n \cdot x^{n-1} \).
2. The derivative of a constant is zero.

Let's apply these rules:

\[
y = 3x^2 + 5x + 6
\]

- The derivative of \( 3x^2 \) is \( 2 \cdot 3x^{2-1} = 6x \).
- The derivative of \( 5x \) is \( 5 \).
- The derivative of the constant \( 6 \) is \( 0 \).

So, the derivative \( y' \) is:

\[
y' = 6x + 5
\]

Would you like a more detailed explanation of these steps, or do you have any further questions?

Here are five related questions you might find helpful:
1. How do you find the derivative of a product of two functions?
2. What is the chain rule in differentiation?
3. How do you differentiate a function that involves a square root?
4. What is the second derivative of \( y = 3x^2 + 5x + 6 \)?
5. How can derivatives be applied to find the slope of a tangent line at a specific point?

**Tip:** Always simplify the function as much as possible before differentiating to make the process easier.

Find the derivative of the function y = 3x^2 + 5x + 6.

Learn how to find the derivative of the polynomial function y = 3x^2 + 5x + 6. This problem uses basic differentiation rules and is suitable for students in Grades 10-12.

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