Let's go through each function and find their derivatives with respect to $x$.

1. $y = 2x + 5$

The derivative of $y$ with respect to $x$ is: $\frac{dy}{dx} = 2$

2. $y = 5$

The derivative of a constant is always zero: $\frac{dy}{dx} = 0$

3. $y = 3e$

Here, $3e$ is a constant (since $e$ is a constant), so its derivative is: $\frac{dy}{dx} = 0$

4. $y = \frac{3}{5}$

Again, this is a constant, so its derivative is: $\frac{dy}{dx} = 0$

5. $y = \sqrt{6}$

$\sqrt{6}$ is also a constant, so its derivative is: $\frac{dy}{dx} = 0$

6. $y = 5x$

The derivative of $y = 5x$ with respect to $x$ is: $\frac{dy}{dx} = 5$

7. $y = \frac{5}{2}x$

Here, the derivative of $y = \frac{5}{2}x$ with respect to $x$ is: $\frac{dy}{dx} = \frac{5}{2}$

Would you like further details or explanations on any of these derivatives? Here are some related questions to explore the topic further:

1. What is the derivative of a function with multiple variables?
2. How do you find the second derivative of a function?
3. Can you explain the chain rule in differentiation?
4. How does the product rule work in calculus?
5. What is the significance of a derivative in real-world applications?

Tip: Remember that the derivative of a constant is always zero, no matter the value of the constant.