6.34. Using the first differential, calculate $\sqrt{25.2}$.
Solution.

$$
f(x+\Delta x) \approx f(x)+f^{\prime}(x) \cdot \Delta x=\sqrt{25}+\frac{1}{2 \sqrt{25}} \cdot 0.2=5.02
$$

## CALCULATION OF HIGHER ORDER DERIVATIVES AND DIFFERENTIALS