題組內容

For questions 1–2, no need to show the calculation process. For questions 3–5, show the calculation and reasoning process. 1. Answer the following questions.

(g) \( (10\%) \) Given \( F(x,y,z) = x^{2}y^{3} + z^{3} + xyz - 3 = 0 \), find \( \partial y / \partial x \) and \( \partial z / \partial x \) at the point \( (x,y,z) = (1,1,1) \).