461. The law of temperature change $T$ of a body depending on time $t$ is given by the equation $T=0.2 t^{2}$. At what rate is this body heating at the moment of time $10 \mathrm{c}$?
Solution. The heating rate of a body is the derivative of temperature $T$ with respect to time $t$:

$$
\frac{d T}{d t}=\left(0.2 t^{2}\right)^{\prime}=0.4 t
$$

Determine the heating rate of the body at $t=10$:

$$
\left(\frac{d T}{d t}\right)_{t=10}=0.4 \cdot 10=4(\text{ deg } / \mathrm{s})
$$