## Thomas' Calculus 13th Edition

$-1.55$
$x=cos(t)=cos1$ when $t=1$ $\frac{dx}{dt}=-sin(t)=-sin1$ when $t=1$ $y=sin(t)=sin1$ when $t=1$ $\frac{dy}{dt}=cos(t)=cos1$ when $t=1$ $z=cos(2t)=cos2$ when $t=1$ $\frac{dz}{dt}=-sin(2t)=-sin2$ when $t=1$ $f(x,y,z)=xy+yz+xz$ $f_{x}=y+z=sin1+cos2$ when $t=1$ $f_{y}=x+z=cos1+cos2$ when $t=1$ $f_{z}=x+y=cos1+sin1$ when $t=1$ $\frac{df}{dt}=f_{x}\frac{dx}{dt}+f_{y}\frac{dy}{dt}+f_{z}\frac{dz}{dt}$ $=(sin1+cos2)(-sin1)+(cos1+cos2)(cos1)+(cos1+sin1)(-sin2)=-1.55$