Suppose w=(x)/(y)+(y)/(z), where x=e^(t), y=2+sin(t), and z=2+cos(4t). Use the chain rule to find (dw)/(dt) as a function of x, y, z, and t. Which of the following options correctly represents (dw)/(dt)?

A. (1)/(y)+(y)/(z)
B. (x)/(y)+(y)/(z)
C. (x)/(y)-(y)/(z)
D. (x)/(y)-(y)/(z)+(z)/(t)