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The image contains a list of exercises that ask to find the derivative of various functions using the limit process. Let's walk through the steps for a few examples:

### Example 11:
**\( f(x) = 7 \)**

Since this is a constant function, its derivative is zero:
\[
f'(x) = 0
\]

### Example 13:
**\( f(x) = -10x \)**

For a linear function \( f(x) = ax \), the derivative is simply the constant coefficient \( a \). Thus:
\[
f'(x) = -10
\]

### Example 17:
**\( f(x) = x^2 + x - 3 \)**

Using the sum and power rules of differentiation:
\[
f'(x) = 2x + 1
\]

### Example 19:
**\( f(x) = x^3 - 12x \)**

Using the power rule:
\[
f'(x) = 3x^2 - 12
\]

### Example 21:
**\( f(x) = \frac{1}{x - 1} \)**

This is a rational function. We rewrite it as \( f(x) = (x - 1)^{-1} \), and then apply the power rule:
\[
f'(x) = -(x - 1)^{-2}
\]
Or equivalently:
\[
f'(x) = -\frac{1}{(x - 1)^2}
\]

Would you like details on any specific problem or steps involved? Here are some further questions that can deepen your understanding:

1. How is the limit definition of a derivative applied to these problems?
2. How does the power rule simplify derivative calculations?
3. Why does the derivative of a constant equal zero?
4. What is the chain rule, and how might it apply to more complex functions?
5. How would you compute the derivative of a product or quotient of two functions?

**Tip:** Understanding the power rule will help you with most polynomial functions and save time in differentiation.

Find the derivative by the limit process for the functions in exercises 11–24.

Learn how to find the derivative of various functions using the limit process. This set of exercises covers differentiation of constants, linear functions, polynomials, and rational functions using the power rule and the limit definition. Suitable for high school students in Grades 10-12.

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