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Assignment5: Problem 1 (1 point) Suppose $w = \frac{x}{y} + \frac{y}{z}$, where $x = e^{2t}$, $y = 2 + \sin(3t)$, and $z = 2 + \cos(6t)$. A) Use the chain rule to find $\frac{dw}{dt}$ as a function of $x$, $y$, $z$, and $t$. Do not rewrite $x$, $y$, and $z$ in terms of $t$, and do not rewrite $e^{2t}$ as $x$. $\frac{dw}{dt} = ([(1/y)(2e^{2t})])+(((-x/y^2)+(1/z))(3\cos(3t)])+([(-y/z^2)*(-6\sin(t))])$ Note: You may want to 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 $\frac{dw}{dt}$ when $t = 0$. Note: You can earn partial credit on this problem.

          Assignment5: Problem 1
(1 point)
Suppose $w = \frac{x}{y} + \frac{y}{z}$, where
$x = e^{2t}$, $y = 2 + \sin(3t)$, and $z = 2 + \cos(6t)$.
A) Use the chain rule to find $\frac{dw}{dt}$ as a function of $x$, $y$, $z$, and $t$. Do not rewrite $x$, $y$, and $z$ in terms of $t$, and do not rewrite $e^{2t}$ as $x$.
$\frac{dw}{dt} = ([(1/y)*(2e^{2t})])+(((-x/y^2)+(1/z))*(3\cos(3t)])+([(-y/z^2)*(-6\sin(t))])$ 
Note: You may want to 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 $\frac{dw}{dt}$ when $t = 0$.
Note: You can earn partial credit on this problem.

Assignment5: Problem 1
(1 point)
Suppose w = (x)/(y) + (y)/(z), where
x = e^2t, y = 2 + sin(3t), and z = 2 + cos(6t).
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 e^2t as x.
(dw)/(dt) = ([(1/y)*(2e^2t)])+(((-x/y^2)+(1/z))*(3cos(3t)])+([(-y/z^2)*(-6sin(t))])
Note: You may want to 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.
Note: You can earn partial credit on this problem.

Added by Lourdes M.

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