Господин Экзамен
Другие калькуляторы
- Производная неявно заданной функции
- Производная параметрической функции
- Частная производная функции
- Исследование функции по шагам
- Интеграл по шагам
- Дифференциальные уравнения по шагам
- Пределы по шагам
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Как пользоваться?
- Производная:
- Производная sqrt(x)+1
- Производная (sin(4*x))^2
- Производная tan(3*x-pi/4)
- Производная x^15
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Идентичные выражения
- log(один +cos(x))^log(x)^ два
- логарифм от (1 плюс косинус от (x)) в степени логарифм от (x) в квадрате
- логарифм от (один плюс косинус от (x)) в степени логарифм от (x) в степени два
- log(1+cos(x))log(x)2
- log1+cosxlogx2
- log(1+cos(x))^log(x)²
- log(1+cos(x)) в степени log(x) в степени 2
- log1+cosx^logx^2
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Похожие выражения
- log(1-cos(x))^log(x)^2
- log(1+cosx)^log(x)^2
Производная log(1+cos(x))^log(x)^2
Решение
Вы ввели
[src]
2
log (x)
(log(1 + cos(x)))
$$\log{\left(\cos{\left(x \right)} + 1 \right)}^{\log{\left(x \right)}^{2}}$$
/ 2 \ d | log (x)| --\(log(1 + cos(x))) / dx
$$\frac{d}{d x} \log{\left(\cos{\left(x \right)} + 1 \right)}^{\log{\left(x \right)}^{2}}$$
Подробное решение
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Не могу найти шаги в поиске этой производной.
Но производная
Ответ:
Первая производная
[src]
2 / 2 \
log (x) |2*log(x)*log(log(1 + cos(x))) log (x)*sin(x) |
(log(1 + cos(x))) *|----------------------------- - ----------------------------|
\ x (1 + cos(x))*log(1 + cos(x))/
$$\left(- \frac{\log{\left(x \right)}^{2} \sin{\left(x \right)}}{\left(\cos{\left(x \right)} + 1\right) \log{\left(\cos{\left(x \right)} + 1 \right)}} + \frac{2 \log{\left(x \right)} \log{\left(\log{\left(\cos{\left(x \right)} + 1 \right)} \right)}}{x}\right) \log{\left(\cos{\left(x \right)} + 1 \right)}^{\log{\left(x \right)}^{2}}$$
Вторая производная
[src]
2 / 2 2 2 2 2 2 \
log (x) |/ 2*log(log(1 + cos(x))) log(x)*sin(x) \ 2 2*log(log(1 + cos(x))) 2*log(x)*log(log(1 + cos(x))) log (x)*cos(x) log (x)*sin (x) log (x)*sin (x) 4*log(x)*sin(x) |
(log(1 + cos(x))) *||- ---------------------- + ----------------------------| *log (x) + ---------------------- - ----------------------------- - ---------------------------- - ----------------------------- - ------------------------------ - ------------------------------|
|\ x (1 + cos(x))*log(1 + cos(x))/ 2 2 (1 + cos(x))*log(1 + cos(x)) 2 2 2 x*(1 + cos(x))*log(1 + cos(x))|
\ x x (1 + cos(x)) *log(1 + cos(x)) (1 + cos(x)) *log (1 + cos(x)) /
$$\left(\left(\frac{\log{\left(x \right)} \sin{\left(x \right)}}{\left(\cos{\left(x \right)} + 1\right) \log{\left(\cos{\left(x \right)} + 1 \right)}} - \frac{2 \log{\left(\log{\left(\cos{\left(x \right)} + 1 \right)} \right)}}{x}\right)^{2} \log{\left(x \right)}^{2} - \frac{\log{\left(x \right)}^{2} \cos{\left(x \right)}}{\left(\cos{\left(x \right)} + 1\right) \log{\left(\cos{\left(x \right)} + 1 \right)}} - \frac{\log{\left(x \right)}^{2} \sin^{2}{\left(x \right)}}{\left(\cos{\left(x \right)} + 1\right)^{2} \log{\left(\cos{\left(x \right)} + 1 \right)}} - \frac{\log{\left(x \right)}^{2} \sin^{2}{\left(x \right)}}{\left(\cos{\left(x \right)} + 1\right)^{2} \log{\left(\cos{\left(x \right)} + 1 \right)}^{2}} - \frac{2 \log{\left(x \right)} \log{\left(\log{\left(\cos{\left(x \right)} + 1 \right)} \right)}}{x^{2}} - \frac{4 \log{\left(x \right)} \sin{\left(x \right)}}{x \left(\cos{\left(x \right)} + 1\right) \log{\left(\cos{\left(x \right)} + 1 \right)}} + \frac{2 \log{\left(\log{\left(\cos{\left(x \right)} + 1 \right)} \right)}}{x^{2}}\right) \log{\left(\cos{\left(x \right)} + 1 \right)}^{\log{\left(x \right)}^{2}}$$
Третья производная
[src]
2 / 3 / 2 2 2 2 2 \ 2 2 3 2 3 2 3 2 2 2 2 \
log (x) | / 2*log(log(1 + cos(x))) log(x)*sin(x) \ 3 6*log(log(1 + cos(x))) / 2*log(log(1 + cos(x))) log(x)*sin(x) \ | 2*log(log(1 + cos(x))) 2*log(x)*log(log(1 + cos(x))) log (x)*cos(x) log (x)*sin (x) log (x)*sin (x) 4*log(x)*sin(x) | 4*log(x)*log(log(1 + cos(x))) log (x)*sin(x) 6*sin(x) 3*log (x)*sin (x) 2*log (x)*sin (x) 2*log (x)*sin (x) 6*cos(x)*log(x) 6*sin (x)*log(x) 6*sin (x)*log(x) 3*log (x)*cos(x)*sin(x) 3*log (x)*cos(x)*sin(x) 6*log(x)*sin(x) |
(log(1 + cos(x))) *|- |- ---------------------- + ----------------------------| *log (x) - ---------------------- + 3*|- ---------------------- + ----------------------------|*|- ---------------------- + ----------------------------- + ---------------------------- + ----------------------------- + ------------------------------ + ------------------------------|*log(x) + ----------------------------- + ---------------------------- - ------------------------------- - ------------------------------ - ----------------------------- - ------------------------------ - ------------------------------ - ------------------------------- - -------------------------------- - ----------------------------- - ------------------------------ + -------------------------------|
| \ x (1 + cos(x))*log(1 + cos(x))/ 3 \ x (1 + cos(x))*log(1 + cos(x))/ | 2 2 (1 + cos(x))*log(1 + cos(x)) 2 2 2 x*(1 + cos(x))*log(1 + cos(x))| 3 (1 + cos(x))*log(1 + cos(x)) 2 3 2 3 3 3 x*(1 + cos(x))*log(1 + cos(x)) 2 2 2 2 2 2 2 |
\ x \ x x (1 + cos(x)) *log(1 + cos(x)) (1 + cos(x)) *log (1 + cos(x)) / x x *(1 + cos(x))*log(1 + cos(x)) (1 + cos(x)) *log (1 + cos(x)) (1 + cos(x)) *log(1 + cos(x)) (1 + cos(x)) *log (1 + cos(x)) x*(1 + cos(x)) *log(1 + cos(x)) x*(1 + cos(x)) *log (1 + cos(x)) (1 + cos(x)) *log(1 + cos(x)) (1 + cos(x)) *log (1 + cos(x)) x *(1 + cos(x))*log(1 + cos(x))/
$$\left(- \left(\frac{\log{\left(x \right)} \sin{\left(x \right)}}{\left(\cos{\left(x \right)} + 1\right) \log{\left(\cos{\left(x \right)} + 1 \right)}} - \frac{2 \log{\left(\log{\left(\cos{\left(x \right)} + 1 \right)} \right)}}{x}\right)^{3} \log{\left(x \right)}^{3} + 3 \left(\frac{\log{\left(x \right)} \sin{\left(x \right)}}{\left(\cos{\left(x \right)} + 1\right) \log{\left(\cos{\left(x \right)} + 1 \right)}} - \frac{2 \log{\left(\log{\left(\cos{\left(x \right)} + 1 \right)} \right)}}{x}\right) \left(\frac{\log{\left(x \right)}^{2} \cos{\left(x \right)}}{\left(\cos{\left(x \right)} + 1\right) \log{\left(\cos{\left(x \right)} + 1 \right)}} + \frac{\log{\left(x \right)}^{2} \sin^{2}{\left(x \right)}}{\left(\cos{\left(x \right)} + 1\right)^{2} \log{\left(\cos{\left(x \right)} + 1 \right)}} + \frac{\log{\left(x \right)}^{2} \sin^{2}{\left(x \right)}}{\left(\cos{\left(x \right)} + 1\right)^{2} \log{\left(\cos{\left(x \right)} + 1 \right)}^{2}} + \frac{2 \log{\left(x \right)} \log{\left(\log{\left(\cos{\left(x \right)} + 1 \right)} \right)}}{x^{2}} + \frac{4 \log{\left(x \right)} \sin{\left(x \right)}}{x \left(\cos{\left(x \right)} + 1\right) \log{\left(\cos{\left(x \right)} + 1 \right)}} - \frac{2 \log{\left(\log{\left(\cos{\left(x \right)} + 1 \right)} \right)}}{x^{2}}\right) \log{\left(x \right)} + \frac{\log{\left(x \right)}^{2} \sin{\left(x \right)}}{\left(\cos{\left(x \right)} + 1\right) \log{\left(\cos{\left(x \right)} + 1 \right)}} - \frac{3 \log{\left(x \right)}^{2} \sin{\left(x \right)} \cos{\left(x \right)}}{\left(\cos{\left(x \right)} + 1\right)^{2} \log{\left(\cos{\left(x \right)} + 1 \right)}} - \frac{2 \log{\left(x \right)}^{2} \sin^{3}{\left(x \right)}}{\left(\cos{\left(x \right)} + 1\right)^{3} \log{\left(\cos{\left(x \right)} + 1 \right)}} - \frac{3 \log{\left(x \right)}^{2} \sin{\left(x \right)} \cos{\left(x \right)}}{\left(\cos{\left(x \right)} + 1\right)^{2} \log{\left(\cos{\left(x \right)} + 1 \right)}^{2}} - \frac{3 \log{\left(x \right)}^{2} \sin^{3}{\left(x \right)}}{\left(\cos{\left(x \right)} + 1\right)^{3} \log{\left(\cos{\left(x \right)} + 1 \right)}^{2}} - \frac{2 \log{\left(x \right)}^{2} \sin^{3}{\left(x \right)}}{\left(\cos{\left(x \right)} + 1\right)^{3} \log{\left(\cos{\left(x \right)} + 1 \right)}^{3}} - \frac{6 \log{\left(x \right)} \cos{\left(x \right)}}{x \left(\cos{\left(x \right)} + 1\right) \log{\left(\cos{\left(x \right)} + 1 \right)}} - \frac{6 \log{\left(x \right)} \sin^{2}{\left(x \right)}}{x \left(\cos{\left(x \right)} + 1\right)^{2} \log{\left(\cos{\left(x \right)} + 1 \right)}} + \frac{4 \log{\left(x \right)} \log{\left(\log{\left(\cos{\left(x \right)} + 1 \right)} \right)}}{x^{3}} - \frac{6 \log{\left(x \right)} \sin^{2}{\left(x \right)}}{x \left(\cos{\left(x \right)} + 1\right)^{2} \log{\left(\cos{\left(x \right)} + 1 \right)}^{2}} + \frac{6 \log{\left(x \right)} \sin{\left(x \right)}}{x^{2} \left(\cos{\left(x \right)} + 1\right) \log{\left(\cos{\left(x \right)} + 1 \right)}} - \frac{6 \log{\left(\log{\left(\cos{\left(x \right)} + 1 \right)} \right)}}{x^{3}} - \frac{6 \sin{\left(x \right)}}{x^{2} \left(\cos{\left(x \right)} + 1\right) \log{\left(\cos{\left(x \right)} + 1 \right)}}\right) \log{\left(\cos{\left(x \right)} + 1 \right)}^{\log{\left(x \right)}^{2}}$$
График