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 x/(1-cos(x))
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Производная acos(e)^x
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Производная log(x+1)
- Производная 2*x+1/5
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Идентичные выражения
- log(tan(x))^(x/ три)
- логарифм от ( тангенс от (x)) в степени (x делить на 3)
- логарифм от ( тангенс от (x)) в степени (x делить на три)
- log(tan(x))(x/3)
- logtanxx/3
- logtanx^x/3
- log(tan(x))^(x разделить на 3)
Производная log(tan(x))^(x/3)
Решение
Вы ввели
[src]
x
-
3
(log(tan(x)))
$$\log{\left(\tan{\left(x \right)} \right)}^{\frac{x}{3}}$$
/ x\ | -| d | 3| --\(log(tan(x))) / dx
$$\frac{d}{d x} \log{\left(\tan{\left(x \right)} \right)}^{\frac{x}{3}}$$
Подробное решение
-
Не могу найти шаги в поиске этой производной.
Но производная
-
Теперь упростим:
Ответ:
Первая производная
[src]
x
- / / 2 \ \
3 |log(log(tan(x))) x*\1 + tan (x)/ |
(log(tan(x))) *|---------------- + --------------------|
\ 3 3*log(tan(x))*tan(x)/
$$\left(\frac{\log{\left(\log{\left(\tan{\left(x \right)} \right)} \right)}}{3} + \frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{3 \log{\left(\tan{\left(x \right)} \right)} \tan{\left(x \right)}}\right) \log{\left(\tan{\left(x \right)} \right)}^{\frac{x}{3}}$$
Вторая производная
[src]
/ / / 2 \ / 2 \ \\
| / 2 \ | 2 x*\1 + tan (x)/ x*\1 + tan (x)/ ||
x | 2 3*\1 + tan (x)/*|-2*x - ------ + --------------- + -------------------||
- |/ / 2 \ \ | tan(x) 2 2 ||
3 || x*\1 + tan (x)/ | \ tan (x) log(tan(x))*tan (x)/|
(log(tan(x))) *||------------------ + log(log(tan(x)))| - -----------------------------------------------------------------------|
\\log(tan(x))*tan(x) / log(tan(x)) /
-----------------------------------------------------------------------------------------------------------------------------------
9
$$\frac{\left(\left(\log{\left(\log{\left(\tan{\left(x \right)} \right)} \right)} + \frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\log{\left(\tan{\left(x \right)} \right)} \tan{\left(x \right)}}\right)^{2} - \frac{3 \left(\tan^{2}{\left(x \right)} + 1\right) \left(- 2 x + \frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan^{2}{\left(x \right)}} + \frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\log{\left(\tan{\left(x \right)} \right)} \tan^{2}{\left(x \right)}} - \frac{2}{\tan{\left(x \right)}}\right)}{\log{\left(\tan{\left(x \right)} \right)}}\right) \log{\left(\tan{\left(x \right)} \right)}^{\frac{x}{3}}}{9}$$
Третья производная
[src]
/ / 2 2 2\ \
| | / 2 \ / 2 \ / 2 \ / 2 \ / 2 \ / 2 \ / 2 \ | / / 2 \ \ / / 2 \ / 2 \ \|
| / 2 \ | 3*\1 + tan (x)/ 4*x*\1 + tan (x)/ 3*\1 + tan (x)/ 2*x*\1 + tan (x)/ 6*x*\1 + tan (x)/ 2*x*\1 + tan (x)/ 3*x*\1 + tan (x)/ | / 2 \ | x*\1 + tan (x)/ | | 2 x*\1 + tan (x)/ x*\1 + tan (x)/ ||
x | 3 9*\1 + tan (x)/*|6 - --------------- + 4*x*tan(x) - ----------------- - ------------------- + ------------------ - ------------------ + -------------------- + -------------------| 9*\1 + tan (x)/*|------------------ + log(log(tan(x)))|*|-2*x - ------ + --------------- + -------------------||
- |/ / 2 \ \ | 2 tan(x) 2 3 log(tan(x))*tan(x) 2 3 3 | \log(tan(x))*tan(x) / | tan(x) 2 2 ||
3 || x*\1 + tan (x)/ | \ tan (x) log(tan(x))*tan (x) tan (x) log (tan(x))*tan (x) log(tan(x))*tan (x)/ \ tan (x) log(tan(x))*tan (x)/|
(log(tan(x))) *||------------------ + log(log(tan(x)))| + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------|
\\log(tan(x))*tan(x) / log(tan(x)) log(tan(x)) /
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
27
$$\frac{\left(\left(\log{\left(\log{\left(\tan{\left(x \right)} \right)} \right)} + \frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\log{\left(\tan{\left(x \right)} \right)} \tan{\left(x \right)}}\right)^{3} - \frac{9 \left(\log{\left(\log{\left(\tan{\left(x \right)} \right)} \right)} + \frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\log{\left(\tan{\left(x \right)} \right)} \tan{\left(x \right)}}\right) \left(\tan^{2}{\left(x \right)} + 1\right) \left(- 2 x + \frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan^{2}{\left(x \right)}} + \frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\log{\left(\tan{\left(x \right)} \right)} \tan^{2}{\left(x \right)}} - \frac{2}{\tan{\left(x \right)}}\right)}{\log{\left(\tan{\left(x \right)} \right)}} + \frac{9 \left(\tan^{2}{\left(x \right)} + 1\right) \left(4 x \tan{\left(x \right)} - \frac{4 x \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} + \frac{2 x \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{\tan^{3}{\left(x \right)}} - \frac{6 x \left(\tan^{2}{\left(x \right)} + 1\right)}{\log{\left(\tan{\left(x \right)} \right)} \tan{\left(x \right)}} + 6 + \frac{3 x \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{\log{\left(\tan{\left(x \right)} \right)} \tan^{3}{\left(x \right)}} - \frac{3 \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan^{2}{\left(x \right)}} + \frac{2 x \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{\log{\left(\tan{\left(x \right)} \right)}^{2} \tan^{3}{\left(x \right)}} - \frac{3 \left(\tan^{2}{\left(x \right)} + 1\right)}{\log{\left(\tan{\left(x \right)} \right)} \tan^{2}{\left(x \right)}}\right)}{\log{\left(\tan{\left(x \right)} \right)}}\right) \log{\left(\tan{\left(x \right)} \right)}^{\frac{x}{3}}}{27}$$
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