Suppose w = [x/y] + [y/z], x = e2 t, y = 2 + sin( 1 t), z = 2 + cos( 3 t ).

A. Use the chain rule to find [dw/dt] as a function of x, y, z, and t. Do not rewrite x, y, and z in terms of t, and do not rewrite e2 t as x.
[dw/dt] = ???
Note: Use exp() for the exponential function. Your answer should be an expression in x, y, z, and t; e.g. "3x - 4y"

B. Use part A to evaluate [dw/dt] when t = 0.
???

Question

Suppose w = [x/y] + [y/z], x = e2 t, y = 2 + sin( 1 t), z = 2 + cos( 3 t ).

A. Use the chain rule to find [dw/dt] as a function of x, y, z, and t. Do not rewrite x, y, and z in terms of t, and do not rewrite e2 t as x. 
[dw/dt] =  ???
Note: Use exp() for the exponential function. Your answer should be an expression in x, y, z, and t; e.g. "3x - 4y"

B. Use part A to evaluate [dw/dt] when t = 0. 
???

turingtest · Answer

x=(e^2)t or x=e^(2t) or x=2et ?

anonymous · Answer

e^(2t)

turingtest · Answer

I'm starting of with
$$dw/dt=[y(dx/dt)-x(dy/dt)]/y^2+[z(dy/dt)-y(dz/dt)]/z^2$$
(not the final answer)
is this the kind of thing that looks like what you've been doing in class?
And what do you mean by exponential as "exp0"?