Example 4. Calculate $y=x^{3}+2 x$, when $x$ varies from 1 to 1.1.
Solution. First, we find the general expression for the differential of this function:

$$
d y=\left(3 x^{2}+2\right) d x
$$

Substituting the values $x=1, d x=\Delta x=1.1-1=0.1$ into the last formula, we obtain the desired value of the differential:

$$
d y=\left(3 \cdot 1^{2}+2\right) 0.1=5 \cdot 0.1=0.5
$$