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The problem asks to find \(\frac{dy}{dx}\) for the equation \(y = 2x\).

### Solution:
Given the equation:
\[ y = 2x \]

To find \(\frac{dy}{dx}\), we differentiate \(y\) with respect to \(x\).

\[ \frac{dy}{dx} = \frac{d}{dx}(2x) \]

The derivative of \(2x\) with respect to \(x\) is \(2\), because:

\[ \frac{d}{dx}(2x) = 2 \]

So, \(\frac{dy}{dx} = 2\).

### Answer:
The correct answer is **2**.

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Would you like more details on how derivatives are calculated? Here are some related questions:

1. What is the derivative of \(y = ax + b\)?
2. How do you find the derivative of a product of two functions?
3. What is the geometric interpretation of \(\frac{dy}{dx}\)?
4. Can \(\frac{dy}{dx}\) be zero? Under what conditions?
5. What is the derivative of a constant function?
6. How do you apply the power rule in differentiation?
7. How do you differentiate trigonometric functions?
8. What is the chain rule in differentiation?

**Tip:** When differentiating, constants multiplied by variables are straightforward—just take the constant and remove the variable.

Explore how to find the derivative dy/dx for the equation y = 2x step-by-step. This problem involves differentiation and covers key concepts such as derivatives of linear functions and the power rule. Suitable for Grades 10-12 students.

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