https://file.aiquickdraw.com/mathbot/file/1730334603654b2lovg1x.jpg

The image appears to be upside down, and the handwriting is a bit faint. After rotating and enhancing the text, here’s the transcription I see:

1. **\( u \) and \( v \) are functions**: Likely an instruction that functions \( u \) and \( v \) are involved in some computation.
2. **Using the product rule**: This suggests that the problem involves differentiation where the product rule is applicable.
3. **\( u' \cdot v + u \cdot v' \)**: This appears to be the formula for the derivative of the product \( u \cdot v \) using the product rule, which states that the derivative of \( u \cdot v \) is given by \( u' \cdot v + u \cdot v' \).
4. **Example given as** \( \frac{d}{dx} (5x) = 5 \cdot x' + x \cdot 5' \).

Please confirm if you need further steps worked out or if there's more specific assistance you require with this problem. 

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Would you like a detailed explanation on using the product rule?

### Related Questions
1. How do you find \( u' \) and \( v' \) when \( u \) and \( v \) are given explicitly?
2. What is the chain rule, and how does it differ from the product rule?
3. How do you apply the product rule to higher-order derivatives?
4. Can the product rule be extended to more than two functions?
5. How can the product rule be used in integration?

### Tip
When using the product rule, remember that the order of differentiation matters: \( u'v + uv' \) is specific to each function's role in the product.

Given two functions u and v, find the derivative of their product using the product rule.

Learn how to apply the product rule to find the derivative of a product of two functions. This problem includes differentiation techniques and the product rule formula. Suitable for advanced high school students in Grades 11-12.

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