Answer
$dz =-2e^{-2x}\cos 2\pi t dx-2\pi e^{-2x}\sin 2\pi tdt$
Work Step by Step
$dz =\displaystyle \frac{\partial z}{\partial x}dx+\frac{\partial z}{\partial t}dt$
$\displaystyle \frac{\partial z}{\partial x}dx=\cos 2\pi t \cdot e^{-2x}(-2)dx=-2e^{-2x}\cos 2\pi t dx$
$\displaystyle \frac{\partial z}{\partial t}dt=e^{-2x}(-\sin 2\pi t)(2\pi)dt=-2\pi e^{-2x}\sin 2\pi tdt$
$dz =-2e^{-2x}\cos 2\pi t dx-2\pi e^{-2x}\sin 2\pi tdt$
