Answer
5
Work Step by Step
$x=2\sqrt t=2$ (t=1)
$\frac{dx}{dt}=\frac{1}{\sqrt t}=1$ (t=1)
$y=t-1+\ln t=0$ (t=1)
$\frac{dy}{dt}=1+\frac{1}{t}=2$ (t=1)
$z=\pi t=\pi$ (t=1)
$\frac{dz}{dt}=\pi$
$w=xe^{y}+ySin(z)-Cos(z)$
$w_{x}=e^{y}=1$ (t=1)
$w_{y}=xe^{y}+Sin(z)=2$ (t=1)
$w_{z}=yCos(z)+Sin(z)=0$ (t=1)
$\frac{dw}{dt}=w_{x}\frac{dx}{dt}+w_{y}\frac{dy}{dt}+w_{z}\frac{dz}{dt}=1+4+0=5$ (t=1)
