Question

Допоможіть будь ласка!!!

Answer 1

Ответ:

1) 7

2) 3.2

3) 0.125

4) $-\frac{1}{48}$

Объяснение:

$1) y = x^7\\y' = 7x^6\\y'(-1) = 7*(-1)^6 = 7*1 = 7\\2) y = x^{\frac{2}{5}}\\y' = x^{\frac{2}{5} } = \frac{2}{5} * x^{-\frac{3}{5} } = \frac{2}{5} * \frac{1}{x^{\frac{3}{5}}} \\y'(32) = \frac{2}{5} * \sqrt[5]{(32)^3} = \frac{2}{5} * \sqrt[5]{(2^5)^3} = \frac{2}{5} * 2^3 = \frac{2^4}{5} = \frac{16}{5} = \frac{32}{10} = 3.2\\3) y = x^{-4}\\y' = -4x^{-5} = \frac{-4}{x^5}\\y'(-2) = \frac{-4}{(-2)^5} = \frac{-4}{-32} = \frac{1}{8} = 0.125$

$4) y = x^{-\frac{1}{3}}\\y' = -\frac{1}{3}x^{-\frac{4}{3}} = -\frac{1}{3}*\frac{1}{{x^{\frac{4}{3}}}}\\y'(8) = -\frac{1}{3}*\frac{1}{\sqrt[3]{8^4}} = -\frac{1}{3}* \frac{1}{\sqrt[3]{(2^3)^4} }} = -\frac{1}{3}* \frac{1}{2^4} = -\frac{1}{3*16} = -\frac{1}{48}$