Express ∂w

∂u and ∂w

∂y as functions of u and y,

Let's express the partial derivatives of \( w \) with respect to \( u \) and \( y \), denoted as \( \frac{\partial w}{\partial u} \) and \( \frac{\partial w}{\partial y} \), as functions of \( u \) and \( y \).

To do this, we need the explicit relationship between \( w \), \( u \), and \( y \). Without this, I can outline general possibilities based on different cases, but typically:

1. If \( w \) is a function of \( u \) and \( y \), i.e., \( w = f(u, y) \), then:
   - \( \frac{\partial w}{\partial u} = \frac{\partial f}{\partial u} \)
   - \( \frac{\partial w}{\partial y} = \frac{\partial f}{\partial y} \)

2. If \( u \) and \( y \) are functions of other variables, say \( x \), then you might use the chain rule:
   - \( \frac{\partial w}{\partial u} = \frac{\partial w}{\partial x} \cdot \frac{\partial x}{\partial u} \)
   - \( \frac{\partial w}{\partial y} = \frac{\partial w}{\partial x} \cdot \frac{\partial x}{\partial y} \)

Would you mind providing the function or equation that links \( w \) with \( u \) and \( y \) for more precise expressions?

### Questions:
1. What specific function relates \( w \), \( u \), and \( y \)?
2. Are there other variables involved in this expression?
3. Is there a chain rule application in the context of this question?
4. Are \( u \) and \( y \) independent or dependent variables in your scenario?
5. Is this part of a larger multivariable calculus problem?

### Tip:
When working with partial derivatives, always identify whether the variables involved are dependent on other variables to properly apply the chain rule.

Express ∂w/∂u and ∂w/∂y as functions of u and y.

Learn how to express the partial derivatives of w with respect to u and y as functions of u and y. This problem explores the concept of partial derivatives, multivariable calculus, and the chain rule. Suitable for undergraduate calculus students.

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