Question

виконайте та поясніть 7 завдання(детальний розвязок)​

Answer 1

1) Д

$y = x \sqrt{2} \\ y' = \sqrt{2} \\ y'(2) = \sqrt{2}$

2) Б

$y = \sqrt{2x} \\ y' = \frac{2}{2 \sqrt{2x} } = \frac{1}{ \sqrt{2x} } \\ y'(2) = \frac{1}{ \sqrt{2 \times 2} } = \frac{ 1 }{ \sqrt{ {2}^{2} } } = \frac{1}{2}$

3) А

$y = \sqrt{x + 2} \\ y' = \frac{1}{2 \sqrt{x + 2} } \\ y'(2) = \frac{1}{2 \sqrt{2 + 2} } = \frac{1}{2 \sqrt{4} } = \frac{1}{2 \times 2} = \frac{1}{4}$

4) В

$y = \sqrt{2x - 3} \\ y' = \frac{2}{2 \sqrt{2x - 3} } = \frac{1}{ \sqrt{2x - 3} } \\ y' (2)= \frac{1}{ \sqrt{2 \times 2 - 3} } = \frac{1}{ \sqrt{4 - 3} } = \frac{1}{ \sqrt{1} } = 1$