題組內容

9. (6%) Let the equation be \( e^z = xyz \). Use implicit differentiation to find \( \frac{\partial z}{\partial x} \) and \( \frac{\partial z}{\partial y} \). 10. \( (20\%) \) Calculate the double integral.

(a) \( (5\%) \) \( \int_0^1\int_0^{e^y}\sqrt{1 + e^y} dxdy \)