Answer
-1
Work Step by Step
$x=e^{t}=1$ ($t=0$)
$\frac{dx}{dt}=e^{t}=1$ ($t=0$)
$y=\ln(t+1)=0$ ($t=0$)
$\frac{dy}{dt}=\frac{1}{t+1}=1$ ($t=0$)
$w=sin(xy+\pi)$
$w_{x}=y\times cos(xy+\pi)=0$ ($t=0$)
$w_{y}=x\times cos(xy+\pi)=-1$ ($t=0$)
$\frac{dw}{dt}=w_{x}\frac{dx}{dt}+w_{y}\frac{dy}{dt}=-1$ at $t=0$
