Exercise 41-44: Find the indicated partial derivative

41 \[ R(s,t) = t e^{\frac{s}{t}}, \qquad R_t (0,1) \]

42

\[f(x, y) = y \sin^{-1}(xy); \quad f_y(1, \tfrac{1}{2})\]

43

\[f(x, y, z) = \ln \left( \frac{1 - \sqrt{x^2 + y^2 + z^2}}{1 + \sqrt{x^2 + y^2 + z^2}} \right); \quad f_y(1, 2, 2)\]

44 \[f(x, y, z) = x^{yz}; \quad f_z(e, 1, 0)\]