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The question asks whether it is **mandatory** to apply the **quotient rule** to find the partial derivative of the given function \( T(x, y) \) with respect to \( y \).

The temperature distribution function is given as:

\[
T(x, y) = \frac{\sin(x) + \cos(y)}{\sin(y) - \cos(y)}
\]

To find the partial derivative of \( T(x, y) \) with respect to \( y \), we must differentiate the quotient of two functions of \( y \). The numerator is \( \sin(x) + \cos(y) \), and the denominator is \( \sin(y) - \cos(y) \). Both terms depend on \( y \).

When differentiating a ratio of functions, the quotient rule is applied. The quotient rule is necessary because you have two functions involving \( y \) (the numerator and the denominator), and to differentiate a fraction, you apply the rule:

\[
\frac{d}{dy} \left( \frac{u(y)}{v(y)} \right) = \frac{v(y) \cdot u'(y) - u(y) \cdot v'(y)}{[v(y)]^2}
\]

Thus, **it is mandatory to apply the quotient rule** in this case. Therefore, the correct answer is **True**.

Would you like a detailed step-by-step derivation of the partial derivative or further clarification? 

Here are five related questions you might explore:
1. What is the quotient rule in differentiation, and how is it derived?
2. Can you apply the product rule to find the partial derivative of a function?
3. What is the geometric interpretation of partial derivatives?
4. How would the partial derivative change if the temperature function \( T(x, y) \) were a product instead of a quotient?
5. How do partial derivatives extend to functions of more than two variables?

**Tip:** The quotient rule is typically required for functions involving division of two differentiable functions. Always check if both parts of the fraction depend on the variable you're differentiating with respect to.

The temperature distribution over a flat plate is given by T(x, y) = (sin(x) + cos(y)) / (sin(y) - cos(y)). Is it mandatory to apply the quotient rule for finding the partial derivative of T with respect to y?

Explore the partial derivative of the temperature distribution function T(x, y) = (sin(x) + cos(y)) / (sin(y) - cos(y)) and understand why applying the quotient rule is mandatory when differentiating with respect to y.

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