Answer
$f_x=-t^2e^{-x}$, $f_y=2te^{-x}$.
Work Step by Step
$f(x,t)=t^2e^{-x}$
To find $f_x$ we treat y as a constant and differentiate with respect to $x$.
$f_x=-t^2e^{-x}$
To find $f_y$ we treat x as a constant and differentiate with respect to $y$.
$f_y=2te^{-x}$
