https://file.aiquickdraw.com/mathbot/file/17245163117753y1qsobw.jpg

To solve this problem using differentiation, I will first extract the mathematical expressions from the image. Let me analyze the content and guide you through the solution.The image contains the following mathematical expression:

\[
\text{Given equation: } y = \left(\frac{\pi}{4}\right) \sin\left(\frac{\pi}{4}x\right) 
\]

It asks to solve it using differentiation, leading to a differentiation of the function.

### Steps for solving by differentiation:
1. **Identify the function**: The function \( y = \left(\frac{\pi}{4}\right) \sin\left(\frac{\pi}{4}x\right) \).
2. **Differentiate with respect to \( x \)**: 

We know that the derivative of \( \sin(ax) \) with respect to \( x \) is \( a \cdot \cos(ax) \).

Thus, the differentiation of the given function is:

\[
\frac{dy}{dx} = \frac{\pi}{4} \cdot \left(\frac{\pi}{4}\right) \cos\left(\frac{\pi}{4}x\right)
\]

Simplifying the constants:

\[
\frac{dy}{dx} = \frac{\pi^2}{16} \cos\left(\frac{\pi}{4}x\right)
\]

This is the result of differentiating the given function.

Would you like a detailed explanation of this differentiation, or do you have any follow-up questions?

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Here are 5 related questions to expand on this topic:
1. What is the general formula for the derivative of trigonometric functions?
2. How does the chain rule apply when differentiating composite functions?
3. What are some real-life applications of sine functions and their derivatives?
4. Can you explain how to handle higher-order derivatives for trigonometric functions?
5. What happens when differentiating sine functions with phase shifts?

**Tip**: Always remember to simplify constants when differentiating, as this can make the solution clearer.

Learn how to solve the problem using differentiation: y = (π/4) sin((π/4)x). This detailed solution covers the differentiation of trigonometric functions, specifically the derivative of sine functions with a constant multiplier. Suitable for advanced high school students and those preparing for calculus exams.

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