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The image you uploaded contains several differentiation problems. I'll guide you through the solutions step by step for each of them.

The goal is to differentiate the given functions with respect to the variable in each case.

### 1. \( y = 12 \)
The derivative of a constant is zero.

\[
\frac{dy}{dx} = 0
\]

---

### 2. \( y = x^7 \)
Use the power rule: \(\frac{d}{dx}(x^n) = n x^{n-1}\).

\[
\frac{dy}{dx} = 7x^6
\]

---

### 3. \( y = \frac{1}{x^5} \)
Rewrite this as \( y = x^{-5} \), then apply the power rule.

\[
\frac{dy}{dx} = -5x^{-6} = -\frac{5}{x^6}
\]

---

### 4. \( y = \sqrt[3]{x} \)
Rewrite this as \( y = x^{\frac{1}{3}} \), and apply the power rule.

\[
\frac{dy}{dx} = \frac{1}{3}x^{-\frac{2}{3}}
\]

---

### 5. \( y = 9\sqrt{x} \)
Rewrite this as \( y = 9x^{\frac{1}{2}} \), and apply the power rule.

\[
\frac{dy}{dx} = 9 \cdot \frac{1}{2}x^{-\frac{1}{2}} = \frac{9}{2}x^{-\frac{1}{2}} = \frac{9}{2\sqrt{x}}
\]

---

### 6. \( y = 9t + 11 \)
Differentiate term by term with respect to \( t \).

\[
\frac{dy}{dt} = 9
\]

---

### 7. \( y = -3t^2 + 2t - 4 \)
Differentiate term by term.

\[
\frac{dy}{dt} = -6t + 2
\]

---

### 8. \( y = x(3x^2 - 9) \)
First, expand the expression: 
\[
y = 3x^3 - 9x
\]
Now differentiate term by term.

\[
\frac{dy}{dx} = 9x^2 - 9
\]

---

### 9. \( y = \frac{4x^3 - 7x + 8}{x} \)
First, simplify the expression by dividing each term by \( x \):
\[
y = 4x^2 - 7 + \frac{8}{x} = 4x^2 - 7 + 8x^{-1}
\]
Now differentiate term by term.

\[
\frac{dy}{dx} = 8x - 8x^{-2} = 8x - \frac{8}{x^2}
\]

---

### 10. \( y = \frac{x^5 - 5x^3 + 2x}{x^3} \)
Simplify the expression by dividing each term by \( x^3 \):
\[
y = x^2 - 5 + \frac{2}{x^2} = x^2 - 5 + 2x^{-2}
\]
Now differentiate term by term.

\[
\frac{dy}{dx} = 2x + 4x^{-3} = 2x + \frac{4}{x^3}
\]

---

If you have any questions or need further details on any of the steps, feel free to ask!

### Relative Questions:
1. How does the power rule apply to negative exponents?
2. What are the general rules for differentiating constant terms?
3. How can we simplify expressions before differentiating them, especially fractions?
4. How would you differentiate a product of two functions using the product rule?
5. What steps should be taken when differentiating functions with radicals?

### Tip:
Always simplify the function as much as possible before applying differentiation rules to make the process easier.

Differentiate the following functions:
1) y = 12
2) y = x^7
3) y = 1/x^5
4) y = cube root of x
5) y = 9 times square root of x
6) y = 9t + 11
7) y = -3t^2 + 2t - 4
8) y = x(3x^2 - 9)
9) y = (4x^3 - 7x + 8) / x
10) y = (x^5 - 5x^3 + 2x) / x^3

This guide covers detailed solutions for differentiating polynomial, radical, and rational functions using the power rule, product rule, and quotient rule. Suitable for advanced high school students (Grades 11-12). Learn how to differentiate various functions, including constants and radicals.

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