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 sec(x)^(2)
- Производная e^(x/3)
- Производная e^(3*x)*sin(2*x)
- Производная 3/x+2*sqrt(x)-e^x
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Идентичные выражения
- (log(cot(x)))^tan(x)
- ( логарифм от ( котангенс от (x))) в степени тангенс от (x)
- (log(cot(x)))tan(x)
- logcotxtanx
- logcotx^tanx
Производная (log(cot(x)))^tan(x)
Решение
Вы ввели
[src]
tan(x) log (cot(x))
$$\log{\left(\cot{\left(x \right)} \right)}^{\tan{\left(x \right)}}$$
d / tan(x) \ --\log (cot(x))/ dx
$$\frac{d}{d x} \log{\left(\cot{\left(x \right)} \right)}^{\tan{\left(x \right)}}$$
Подробное решение
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Не могу найти шаги в поиске этой производной.
Но производная
Ответ:
Первая производная
[src]
/ / 2 \ \
tan(x) |/ 2 \ \-1 - cot (x)/*tan(x)|
log (cot(x))*|\1 + tan (x)/*log(log(cot(x))) + ---------------------|
\ cot(x)*log(cot(x)) /
$$\left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(\log{\left(\cot{\left(x \right)} \right)} \right)} + \frac{\left(- \cot^{2}{\left(x \right)} - 1\right) \tan{\left(x \right)}}{\log{\left(\cot{\left(x \right)} \right)} \cot{\left(x \right)}}\right) \log{\left(\cot{\left(x \right)} \right)}^{\tan{\left(x \right)}}$$
Вторая производная
[src]
/ 2 2 2 \
|/ / 2 \ \ / 2 \ / 2 \ / 2 \ / 2 \ / 2 \|
tan(x) ||/ 2 \ \1 + cot (x)/*tan(x)| 2*\1 + cot (x)/*tan(x) / 2 \ \1 + cot (x)/ *tan(x) \1 + cot (x)/ *tan(x) 2*\1 + cot (x)/*\1 + tan (x)/|
log (cot(x))*||\1 + tan (x)/*log(log(cot(x))) - --------------------| + ---------------------- + 2*\1 + tan (x)/*log(log(cot(x)))*tan(x) - --------------------- - --------------------- - -----------------------------|
|\ cot(x)*log(cot(x)) / log(cot(x)) 2 2 2 cot(x)*log(cot(x)) |
\ cot (x)*log(cot(x)) cot (x)*log (cot(x)) /
$$\left(2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(\log{\left(\cot{\left(x \right)} \right)} \right)} \tan{\left(x \right)} + \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(\log{\left(\cot{\left(x \right)} \right)} \right)} - \frac{\left(\cot^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}}{\log{\left(\cot{\left(x \right)} \right)} \cot{\left(x \right)}}\right)^{2} + \frac{2 \left(\cot^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}}{\log{\left(\cot{\left(x \right)} \right)}} - \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right) \left(\cot^{2}{\left(x \right)} + 1\right)}{\log{\left(\cot{\left(x \right)} \right)} \cot{\left(x \right)}} - \frac{\left(\cot^{2}{\left(x \right)} + 1\right)^{2} \tan{\left(x \right)}}{\log{\left(\cot{\left(x \right)} \right)} \cot^{2}{\left(x \right)}} - \frac{\left(\cot^{2}{\left(x \right)} + 1\right)^{2} \tan{\left(x \right)}}{\log{\left(\cot{\left(x \right)} \right)}^{2} \cot^{2}{\left(x \right)}}\right) \log{\left(\cot{\left(x \right)} \right)}^{\tan{\left(x \right)}}$$
Третья производная
[src]
/ 3 / 2 2 \ 2 2 3 3 3 2 2 \
|/ / 2 \ \ / / 2 \ \ | / 2 \ / 2 \ / 2 \ / 2 \ / 2 \| 2 / 2 \ / 2 \ / 2 \ / 2 \ / 2 \ / 2 \ / 2 \ / 2 \ / 2 \ / 2 \ / 2 \ / 2 \ / 2 \ / 2 \ |
tan(x) ||/ 2 \ \1 + cot (x)/*tan(x)| |/ 2 \ \1 + cot (x)/*tan(x)| | 2*\1 + cot (x)/*tan(x) / 2 \ \1 + cot (x)/ *tan(x) \1 + cot (x)/ *tan(x) 2*\1 + cot (x)/*\1 + tan (x)/| / 2 \ 2 / 2 \ 6*\1 + cot (x)/*\1 + tan (x)/ 4*\1 + cot (x)/*cot(x)*tan(x) 3*\1 + cot (x)/ *\1 + tan (x)/ 3*\1 + cot (x)/ *\1 + tan (x)/ 3*\1 + cot (x)/ *tan(x) 2*\1 + cot (x)/ *tan(x) 2*\1 + cot (x)/ *tan(x) 4*\1 + cot (x)/ *tan(x) 6*\1 + cot (x)/ *tan(x) 6*\1 + cot (x)/*\1 + tan (x)/*tan(x)|
log (cot(x))*||\1 + tan (x)/*log(log(cot(x))) - --------------------| - 3*|\1 + tan (x)/*log(log(cot(x))) - --------------------|*|- ---------------------- - 2*\1 + tan (x)/*log(log(cot(x)))*tan(x) + --------------------- + --------------------- + -----------------------------| + 2*\1 + tan (x)/ *log(log(cot(x))) + 4*tan (x)*\1 + tan (x)/*log(log(cot(x))) + ----------------------------- - ----------------------------- - ------------------------------ - ------------------------------ - ----------------------- - ----------------------- - ----------------------- + ----------------------- + ----------------------- - ------------------------------------|
|\ cot(x)*log(cot(x)) / \ cot(x)*log(cot(x)) / | log(cot(x)) 2 2 2 cot(x)*log(cot(x)) | log(cot(x)) log(cot(x)) 2 2 2 3 2 3 3 3 cot(x)*log(cot(x)) 2 cot(x)*log(cot(x)) |
\ \ cot (x)*log(cot(x)) cot (x)*log (cot(x)) / cot (x)*log(cot(x)) cot (x)*log (cot(x)) cot (x)*log (cot(x)) cot (x)*log(cot(x)) cot (x)*log (cot(x)) cot(x)*log (cot(x)) /
$$\left(4 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(\log{\left(\cot{\left(x \right)} \right)} \right)} \tan^{2}{\left(x \right)} + \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(\log{\left(\cot{\left(x \right)} \right)} \right)} - \frac{\left(\cot^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}}{\log{\left(\cot{\left(x \right)} \right)} \cot{\left(x \right)}}\right)^{3} + 2 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \log{\left(\log{\left(\cot{\left(x \right)} \right)} \right)} - 3 \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(\log{\left(\cot{\left(x \right)} \right)} \right)} - \frac{\left(\cot^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}}{\log{\left(\cot{\left(x \right)} \right)} \cot{\left(x \right)}}\right) \left(- 2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(\log{\left(\cot{\left(x \right)} \right)} \right)} \tan{\left(x \right)} - \frac{2 \left(\cot^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}}{\log{\left(\cot{\left(x \right)} \right)}} + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right) \left(\cot^{2}{\left(x \right)} + 1\right)}{\log{\left(\cot{\left(x \right)} \right)} \cot{\left(x \right)}} + \frac{\left(\cot^{2}{\left(x \right)} + 1\right)^{2} \tan{\left(x \right)}}{\log{\left(\cot{\left(x \right)} \right)} \cot^{2}{\left(x \right)}} + \frac{\left(\cot^{2}{\left(x \right)} + 1\right)^{2} \tan{\left(x \right)}}{\log{\left(\cot{\left(x \right)} \right)}^{2} \cot^{2}{\left(x \right)}}\right) - \frac{4 \left(\cot^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} \cot{\left(x \right)}}{\log{\left(\cot{\left(x \right)} \right)}} - \frac{6 \left(\tan^{2}{\left(x \right)} + 1\right) \left(\cot^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}}{\log{\left(\cot{\left(x \right)} \right)} \cot{\left(x \right)}} + \frac{6 \left(\tan^{2}{\left(x \right)} + 1\right) \left(\cot^{2}{\left(x \right)} + 1\right)}{\log{\left(\cot{\left(x \right)} \right)}} + \frac{4 \left(\cot^{2}{\left(x \right)} + 1\right)^{2} \tan{\left(x \right)}}{\log{\left(\cot{\left(x \right)} \right)} \cot{\left(x \right)}} - \frac{3 \left(\tan^{2}{\left(x \right)} + 1\right) \left(\cot^{2}{\left(x \right)} + 1\right)^{2}}{\log{\left(\cot{\left(x \right)} \right)} \cot^{2}{\left(x \right)}} - \frac{2 \left(\cot^{2}{\left(x \right)} + 1\right)^{3} \tan{\left(x \right)}}{\log{\left(\cot{\left(x \right)} \right)} \cot^{3}{\left(x \right)}} + \frac{6 \left(\cot^{2}{\left(x \right)} + 1\right)^{2} \tan{\left(x \right)}}{\log{\left(\cot{\left(x \right)} \right)}^{2} \cot{\left(x \right)}} - \frac{3 \left(\tan^{2}{\left(x \right)} + 1\right) \left(\cot^{2}{\left(x \right)} + 1\right)^{2}}{\log{\left(\cot{\left(x \right)} \right)}^{2} \cot^{2}{\left(x \right)}} - \frac{3 \left(\cot^{2}{\left(x \right)} + 1\right)^{3} \tan{\left(x \right)}}{\log{\left(\cot{\left(x \right)} \right)}^{2} \cot^{3}{\left(x \right)}} - \frac{2 \left(\cot^{2}{\left(x \right)} + 1\right)^{3} \tan{\left(x \right)}}{\log{\left(\cot{\left(x \right)} \right)}^{3} \cot^{3}{\left(x \right)}}\right) \log{\left(\cot{\left(x \right)} \right)}^{\tan{\left(x \right)}}$$
График