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.
