The image you've uploaded appears to contain a set of partial derivative problems. Here is the translated text of the problems:

1. Find the partial derivatives of each function with respect to the independent variables.

a) $z = \frac{2x}{\sqrt{y}} - \frac{\sqrt{y}}{x}$

b) $z = \arcsin\left(\frac{\sqrt{y}}{x}\right)$

c) $z = \text{arccot}\left(\frac{2y}{xy - 1}\right)$

Would you like to proceed with solving these partial derivatives? Let me know if you'd like any further details or explanations!