題組內容

2. Answer the following questions:

2.8 Suppose that the three variables \( x, y \), and \( z \) satisfy \( x^3 + y^2 + z = 3 \) and \( x \cdot y^2 \cdot z^3 = 1 \). Then \( \frac{dx}{dz} = \underline{\quad (5\%)} \) and \( \frac{dy}{dz} = \underline{\quad (5\%)} \) at the point \( (x, y, z) = (1, 1, 1) \).