Производная функции/ От одной переменной/ y' = ((1-log(x))^(tan(x)))'

Производная (1-log(x))^(tan(x))

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()'

– производная -го порядка в точке

Примеры

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Кусочно-заданная:

{ кусочно-заданную функцию ввести здесь.

Решение

Вы ввели [src]
            tan(x)
(1 - log(x))
$$\left(- \log{\left (x \right )} + 1\right)^{\tan{\left (x \right )}}$$
Подробное решение

  1. Не могу найти шаги в поиске этой производной.

    Но производная

Ответ:

График
Первая производная [src]
            tan(x) //       2   \                       tan(x)    \
(1 - log(x))      *|\1 + tan (x)/*log(1 - log(x)) - --------------|
                   \                                x*(1 - log(x))/
$$\left(\left(\tan^{2}{\left (x \right )} + 1\right) \log{\left (- \log{\left (x \right )} + 1 \right )} - \frac{\tan{\left (x \right )}}{x \left(- \log{\left (x \right )} + 1\right)}\right) \left(- \log{\left (x \right )} + 1\right)^{\tan{\left (x \right )}}$$
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Вторая производная [src]
                   /                                                 2                                            /       2   \                                         \
            tan(x) |//       2   \                        tan(x)    \         tan(x)              tan(x)        2*\1 + tan (x)/     /       2   \                       |
(1 - log(x))      *||\1 + tan (x)/*log(1 - log(x)) + ---------------|  - ---------------- - ----------------- + --------------- + 2*\1 + tan (x)/*log(1 - log(x))*tan(x)|
                   |\                                x*(-1 + log(x))/     2                  2              2   x*(-1 + log(x))                                         |
                   \                                                     x *(-1 + log(x))   x *(-1 + log(x))                                                            /
$$\left(- \log{\left (x \right )} + 1\right)^{\tan{\left (x \right )}} \left(\left(\left(\tan^{2}{\left (x \right )} + 1\right) \log{\left (- \log{\left (x \right )} + 1 \right )} + \frac{\tan{\left (x \right )}}{x \left(\log{\left (x \right )} - 1\right)}\right)^{2} + 2 \left(\tan^{2}{\left (x \right )} + 1\right) \log{\left (- \log{\left (x \right )} + 1 \right )} \tan{\left (x \right )} + \frac{2 \tan^{2}{\left (x \right )} + 2}{x \left(\log{\left (x \right )} - 1\right)} - \frac{\tan{\left (x \right )}}{x^{2} \left(\log{\left (x \right )} - 1\right)} - \frac{\tan{\left (x \right )}}{x^{2} \left(\log{\left (x \right )} - 1\right)^{2}}\right)$$
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Третья производная [src]
                   /                                                 3                  2                                                                       /                                           /       2   \                                         \     /       2   \       /       2   \                                                                                                           /       2   \       \
            tan(x) |//       2   \                        tan(x)    \      /       2   \                      //       2   \                        tan(x)    \ |       tan(x)              tan(x)        2*\1 + tan (x)/     /       2   \                       |   3*\1 + tan (x)/     3*\1 + tan (x)/        2*tan(x)            2*tan(x)            3*tan(x)            2    /       2   \                   6*\1 + tan (x)/*tan(x)|
(1 - log(x))      *||\1 + tan (x)/*log(1 - log(x)) + ---------------|  + 2*\1 + tan (x)/ *log(1 - log(x)) + 3*|\1 + tan (x)/*log(1 - log(x)) + ---------------|*|- ---------------- - ----------------- + --------------- + 2*\1 + tan (x)/*log(1 - log(x))*tan(x)| - ---------------- - ----------------- + ---------------- + ----------------- + ----------------- + 4*tan (x)*\1 + tan (x)/*log(1 - log(x)) + ----------------------|
                   |\                                x*(-1 + log(x))/                                         \                                x*(-1 + log(x))/ |   2                  2              2   x*(-1 + log(x))                                         |    2                  2              2    3                  3              3    3              2                                                x*(-1 + log(x))    |
                   \                                                                                                                                            \  x *(-1 + log(x))   x *(-1 + log(x))                                                            /   x *(-1 + log(x))   x *(-1 + log(x))    x *(-1 + log(x))   x *(-1 + log(x))    x *(-1 + log(x))                                                                    /
$$\left(- \log{\left (x \right )} + 1\right)^{\tan{\left (x \right )}} \left(\left(\left(\tan^{2}{\left (x \right )} + 1\right) \log{\left (- \log{\left (x \right )} + 1 \right )} + \frac{\tan{\left (x \right )}}{x \left(\log{\left (x \right )} - 1\right)}\right)^{3} + 3 \left(\left(\tan^{2}{\left (x \right )} + 1\right) \log{\left (- \log{\left (x \right )} + 1 \right )} + \frac{\tan{\left (x \right )}}{x \left(\log{\left (x \right )} - 1\right)}\right) \left(2 \left(\tan^{2}{\left (x \right )} + 1\right) \log{\left (- \log{\left (x \right )} + 1 \right )} \tan{\left (x \right )} + \frac{2 \tan^{2}{\left (x \right )} + 2}{x \left(\log{\left (x \right )} - 1\right)} - \frac{\tan{\left (x \right )}}{x^{2} \left(\log{\left (x \right )} - 1\right)} - \frac{\tan{\left (x \right )}}{x^{2} \left(\log{\left (x \right )} - 1\right)^{2}}\right) + 2 \left(\tan^{2}{\left (x \right )} + 1\right)^{2} \log{\left (- \log{\left (x \right )} + 1 \right )} + 4 \left(\tan^{2}{\left (x \right )} + 1\right) \log{\left (- \log{\left (x \right )} + 1 \right )} \tan^{2}{\left (x \right )} + \frac{6 \left(\tan^{2}{\left (x \right )} + 1\right) \tan{\left (x \right )}}{x \left(\log{\left (x \right )} - 1\right)} - \frac{3 \tan^{2}{\left (x \right )} + 3}{x^{2} \left(\log{\left (x \right )} - 1\right)} - \frac{3 \tan^{2}{\left (x \right )} + 3}{x^{2} \left(\log{\left (x \right )} - 1\right)^{2}} + \frac{2 \tan{\left (x \right )}}{x^{3} \left(\log{\left (x \right )} - 1\right)} + \frac{3 \tan{\left (x \right )}}{x^{3} \left(\log{\left (x \right )} - 1\right)^{2}} + \frac{2 \tan{\left (x \right )}}{x^{3} \left(\log{\left (x \right )} - 1\right)^{3}}\right)$$
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