Господин Экзамен

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(log(x))^e^sin(x)
Производная функции/ (log(x))^e^sin(x)

Производная (log(x))^e^sin(x)

Функция f() - производная -го порядка в точке
v

График:

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Кусочно-заданная:

Решение

Вы ввели [src] 
        / sin(x)\
        \e      /
(log(x))
$$\log{\left(x \right)}^{e^{\sin{\left(x \right)}}}$$ 
  /        / sin(x)\\
d |        \e      /|
--\(log(x))         /
dx
$$\frac{d}{d x} \log{\left(x \right)}^{e^{\sin{\left(x \right)}}}$$
Преобразовать
Подробное решение

  1. Не могу найти шаги в поиске этой производной.

    Но производная

Ответ:

График
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Первая производная [src] 
        / sin(x)\ / sin(x)                              \
        \e      / |e                  sin(x)            |
(log(x))         *|-------- + cos(x)*e      *log(log(x))|
                  \x*log(x)                             /
$$\left(e^{\sin{\left(x \right)}} \log{\left(\log{\left(x \right)} \right)} \cos{\left(x \right)} + \frac{e^{\sin{\left(x \right)}}}{x \log{\left(x \right)}}\right) \log{\left(x \right)}^{e^{\sin{\left(x \right)}}}$$
Упростить
Вторая производная [src] 
        / sin(x)\ /                               2                                                                                       \        
        \e      / |/   1                         \   sin(x)      2                      1           1                             2*cos(x)|  sin(x)
(log(x))         *||-------- + cos(x)*log(log(x))| *e       + cos (x)*log(log(x)) - --------- - ---------- - log(log(x))*sin(x) + --------|*e      
                  |\x*log(x)                     /                                   2           2    2                           x*log(x)|        
                  \                                                                 x *log(x)   x *log (x)                                /
$$\left(\left(\log{\left(\log{\left(x \right)} \right)} \cos{\left(x \right)} + \frac{1}{x \log{\left(x \right)}}\right)^{2} e^{\sin{\left(x \right)}} + \log{\left(\log{\left(x \right)} \right)} \cos^{2}{\left(x \right)} - \log{\left(\log{\left(x \right)} \right)} \sin{\left(x \right)} + \frac{2 \cos{\left(x \right)}}{x \log{\left(x \right)}} - \frac{1}{x^{2} \log{\left(x \right)}} - \frac{1}{x^{2} \log{\left(x \right)}^{2}}\right) e^{\sin{\left(x \right)}} \log{\left(x \right)}^{e^{\sin{\left(x \right)}}}$$
Упростить
Третья производная [src] 
        / sin(x)\ /                               3                                                                                                                                                                                                                                                                                                2   \        
        \e      / |/   1                         \   2*sin(x)      3                                           2           2            3        3*sin(x)    3*cos(x)    3*cos(x)      /   1                         \ /    1           1                                2                  2*cos(x)\  sin(x)                                 3*cos (x)|  sin(x)
(log(x))         *||-------- + cos(x)*log(log(x))| *e         + cos (x)*log(log(x)) - cos(x)*log(log(x)) + --------- + ---------- + ---------- - -------- - --------- - ---------- - 3*|-------- + cos(x)*log(log(x))|*|--------- + ---------- + log(log(x))*sin(x) - cos (x)*log(log(x)) - --------|*e       - 3*cos(x)*log(log(x))*sin(x) + ---------|*e      
                  |\x*log(x)                     /                                                          3           3    3       3    2      x*log(x)    2           2    2        \x*log(x)                     / | 2           2    2                                                 x*log(x)|                                          x*log(x)|        
                  \                                                                                        x *log(x)   x *log (x)   x *log (x)              x *log(x)   x *log (x)                                     \x *log(x)   x *log (x)                                                      /                                                  /
$$\left(\left(\log{\left(\log{\left(x \right)} \right)} \cos{\left(x \right)} + \frac{1}{x \log{\left(x \right)}}\right)^{3} e^{2 \sin{\left(x \right)}} + \log{\left(\log{\left(x \right)} \right)} \cos^{3}{\left(x \right)} - 3 \left(\log{\left(\log{\left(x \right)} \right)} \cos{\left(x \right)} + \frac{1}{x \log{\left(x \right)}}\right) \left(- \log{\left(\log{\left(x \right)} \right)} \cos^{2}{\left(x \right)} + \log{\left(\log{\left(x \right)} \right)} \sin{\left(x \right)} - \frac{2 \cos{\left(x \right)}}{x \log{\left(x \right)}} + \frac{1}{x^{2} \log{\left(x \right)}} + \frac{1}{x^{2} \log{\left(x \right)}^{2}}\right) e^{\sin{\left(x \right)}} - 3 \log{\left(\log{\left(x \right)} \right)} \sin{\left(x \right)} \cos{\left(x \right)} - \log{\left(\log{\left(x \right)} \right)} \cos{\left(x \right)} + \frac{3 \cos^{2}{\left(x \right)}}{x \log{\left(x \right)}} - \frac{3 \sin{\left(x \right)}}{x \log{\left(x \right)}} - \frac{3 \cos{\left(x \right)}}{x^{2} \log{\left(x \right)}} - \frac{3 \cos{\left(x \right)}}{x^{2} \log{\left(x \right)}^{2}} + \frac{2}{x^{3} \log{\left(x \right)}} + \frac{3}{x^{3} \log{\left(x \right)}^{2}} + \frac{2}{x^{3} \log{\left(x \right)}^{3}}\right) e^{\sin{\left(x \right)}} \log{\left(x \right)}^{e^{\sin{\left(x \right)}}}$$
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Производная (log(x))^e^sin(x)
    © Господин Экзамен – Калькулятор