#### Answer

$$f_x = -t^2e^{-x}.$$
$$f_t = 2te^{-x}.$$

#### Work Step by Step

To find $f_x$, we treat $t$ as a constant and differentiate with respect to $x$. Thus
$$f_x = t^2 \cdot -e^{-x} = -t^2e^{-x}.$$
Similarly, to find $f_t$, we treat $x$ as constant and differentiate with respect to $t$. Thus
$$f_t = 2te^{-x}.$$