https://file.aiquickdraw.com/mathbot/file/17249690031049rzz0env.jpg

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.

Explore how to find derivatives of functions step-by-step. Learn the rules for derivatives of constants and linear functions. Suitable for Grades 11-12 students studying calculus.

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