6.39. Find the first three differentials of the function $y=$ $=x^{2}-2 x+3$.
Solution.

$$
\begin{aligned}
& d y=\left(x^{2}-2 x+3\right)^{\prime} d x=(2 x-2) d x \\
& d^{2} y=(2 x-2)^{\prime}(d x)^{2}=2(d x)^{2} \\
& d^{3} y=(2)^{\prime}(d x)^{3}=0 \cdot(d x)^{3}=0 .
\end{aligned}
$$