Suppose $\displaystyle f(x,t) = e^{-5t}\sin\!\left(x+4t\right)$.

(a) At any point $(x,t)$, the differential is
$df =$

(b) At the point $(-2,0)$, the differential is
$df =$

(c) At the point $(-2,0)$ with $dx = 0.5$ and $dt = -0.3$, the differential is
$df =$