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The image provides an explanation of parametric functions and their derivatives with respect to a parameter \( t \), along with an example problem and a practice problem. Here's a breakdown of the content:

### Key Concepts:
- Parametric functions involve a parameter \( t \), and the goal is to find the derivative of \( y \) with respect to \( x \), denoted as \( \frac{dy}{dx} \), by calculating the derivatives with respect to \( t \).
- Formula:
  \[
  \frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}}
  \]

### Example Problem:
- Given: 
  \[
  x(t) = t^2 + 1 \quad \text{and} \quad y(t) = t^3
  \]
  Find \( \frac{dy}{dx} \).

- Solution:
  - First, compute the derivatives with respect to \( t \):
    \[
    \frac{dx}{dt} = 2t, \quad \frac{dy}{dt} = 3t^2
    \]
  - Then, apply the formula:
    \[
    \frac{dy}{dx} = \frac{3t^2}{2t} = \frac{3t}{2}
    \]

### Practice Problem:
- Given:
  \[
  x(t) = \sin(t) \quad \text{and} \quad y(t) = \cos(t)
  \]
  Find \( \frac{dy}{dx} \).

---

Let's solve the practice problem:

1. Compute the derivatives with respect to \( t \):
   - \( \frac{dx}{dt} = \cos(t) \)
   - \( \frac{dy}{dt} = -\sin(t) \)

2. Apply the formula for \( \frac{dy}{dx} \):
   \[
   \frac{dy}{dx} = \frac{-\sin(t)}{\cos(t)} = -\tan(t)
   \]

Thus, the solution to the practice problem is \( \frac{dy}{dx} = -\tan(t) \).

---

Would you like more details on any part of the solution or further explanation? Here are some related questions:

1. How do you apply the chain rule when working with parametric equations?
2. Can parametric functions be expressed as implicit functions?
3. What happens when the derivatives \( \frac{dx}{dt} \) and \( \frac{dy}{dt} \) involve trigonometric functions?
4. How can parametric equations be used to describe curves in physics?
5. What are some applications of parametric differentiation in real-world problems?

**Tip:** Always ensure that \( \frac{dx}{dt} \neq 0 \) to avoid division by zero when calculating \( \frac{dy}{dx} \).

Soal Latihan: Jika x(t) = sin(t) dan y(t) = cos(t), hitung dy/dx.

Solve a parametric differentiation problem where x(t) = sin(t) and y(t) = cos(t). Learn how to apply the chain rule and compute dy/dx step-by-step for high school students in Grades 11-12.

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