Задача №861.
Найти производную функции

    \[ y= \sqrt [3] {1+ \sqrt [3] {1+ \sqrt [3] {x}}} \]

Решение:

    \[ y'= \frac {1}{3 \sqrt [3]{(1+\sqrt [3]{1+\sqrt [3] {x}})^2}} \frac {1}{3 \sqrt [3]{(1+\sqrt [3]{x})^2}} \frac {1}{ 3 \sqrt [3] {x^2}} \]

    \[ y'= \frac {1}{27 \sqrt [3]{x^2(1+\sqrt [3]{x})^2} \sqrt [3]{(1+ \sqrt [3] {1+\sqrt [3] {x}})^2}} \]

    \[p_{0} = \frac{1}{\frac{1.5^{0}}{0!} + \frac{1.5^{1}}{1!} + \frac{1.5^{2}}{2!} + \frac{1.5^{3}}{3!} + \frac{1.5^{3+1}}{3!\left(3 - 1.5\right)}\left(1 - \left(\frac{1.5}{3}\right)^{8}\right)} = 0.211\]

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