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The worksheet you provided seems to involve applying the **chain rule (Kettenregel)** for differentiation. The table contains functions \( f(x) = u(v(x)) \), where you're expected to compute the outer and inner functions \( u(x) \) and \( v(x) \), their derivatives, and finally the derivative \( f'(x) \).

Here’s the process you can follow for each function:

1. Identify the outer function \( u(x) \) and the inner function \( v(x) \).
2. Compute the derivative of the outer function, \( u'(x) \), and the inner function, \( v'(x) \).
3. Apply the chain rule: 
   \[
   f'(x) = u'(v(x)) \cdot v'(x)
   \]

### Let’s go through the first example step by step.

#### 1. Function: \( f(x) = (2x + 5)^3 \)
- **Outer function**: \( u(x) = x^3 \)
- **Inner function**: \( v(x) = 2x + 5 \)

Now, differentiate:
- \( u'(x) = 3x^2 \)
- \( v'(x) = 2 \)

Finally, applying the chain rule:
\[
f'(x) = 3(2x + 5)^2 \cdot 2 = 6(2x + 5)^2
\]

Would you like to go through another example from the worksheet or clarify anything? I can fill out the entire table or focus on specific rows if you prefer.

Here are five related questions:
1. What is the chain rule in differentiation?
2. How do you differentiate a composite function?
3. What is the difference between the outer and inner functions in the chain rule?
4. How do you apply the power rule in differentiation?
5. How do trigonometric functions apply in chain rule differentiation?

**Tip:** When using the chain rule, always differentiate the outer function first and multiply it by the derivative of the inner function.

The user submitted a worksheet on the chain rule (Kettenregel) for differentiation, asking for assistance in solving or filling out the table.

This worksheet provides exercises on applying the chain rule for differentiating composite functions. It includes problems involving polynomial and trigonometric functions, designed for Grades 11-12 students learning calculus.

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