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
- (cot(x))^tan(x)
- ( котангенс от (x)) в степени тангенс от (x)
- (cot(x))tan(x)
- cotxtanx
- cotx^tanx
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Похожие выражения
- (log(cot(x)))^tan(x)
- cot(x)^tan(x)
Производная (cot(x))^tan(x)
Решение
Вы ввели
[src]
tan(x) cot (x)
$$\cot^{\tan{\left(x \right)}}{\left(x \right)}$$
d / tan(x) \ --\cot (x)/ dx
$$\frac{d}{d x} \cot^{\tan{\left(x \right)}}{\left(x \right)}$$
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)|
cot (x)*|\1 + tan (x)/*log(cot(x)) + ---------------------|
\ cot(x) /
$$\left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(\cot{\left(x \right)} \right)} + \frac{\left(- \cot^{2}{\left(x \right)} - 1\right) \tan{\left(x \right)}}{\cot{\left(x \right)}}\right) \cot^{\tan{\left(x \right)}}{\left(x \right)}$$
Вторая производная
[src]
/ 2 2 \
|/ / 2 \ \ / 2 \ / 2 \ / 2 \ |
tan(x) ||/ 2 \ \1 + cot (x)/*tan(x)| / 2 \ \1 + cot (x)/ *tan(x) 2*\1 + cot (x)/*\1 + tan (x)/ / 2 \ |
cot (x)*||\1 + tan (x)/*log(cot(x)) - --------------------| + 2*\1 + cot (x)/*tan(x) - --------------------- - ----------------------------- + 2*\1 + tan (x)/*log(cot(x))*tan(x)|
|\ cot(x) / 2 cot(x) |
\ cot (x) /
$$\left(2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(\cot{\left(x \right)} \right)} \tan{\left(x \right)} + \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(\cot{\left(x \right)} \right)} - \frac{\left(\cot^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}}{\cot{\left(x \right)}}\right)^{2} + 2 \left(\cot^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} - \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right) \left(\cot^{2}{\left(x \right)} + 1\right)}{\cot{\left(x \right)}} - \frac{\left(\cot^{2}{\left(x \right)} + 1\right)^{2} \tan{\left(x \right)}}{\cot^{2}{\left(x \right)}}\right) \cot^{\tan{\left(x \right)}}{\left(x \right)}$$
Третья производная
[src]
/ 3 / 2 \ 2 3 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 \ 2*\1 + cot (x)/*\1 + tan (x)/| / 2 \ / 2 \ / 2 \ / 2 \ 3*\1 + cot (x)/ *\1 + tan (x)/ 2*\1 + cot (x)/ *tan(x) 4*\1 + cot (x)/ *tan(x) 2 / 2 \ 6*\1 + cot (x)/*\1 + tan (x)/*tan(x)|
cot (x)*||\1 + tan (x)/*log(cot(x)) - --------------------| - 3*|\1 + tan (x)/*log(cot(x)) - --------------------|*|- 2*\1 + cot (x)/*tan(x) + --------------------- - 2*\1 + tan (x)/*log(cot(x))*tan(x) + -----------------------------| + 2*\1 + tan (x)/ *log(cot(x)) + 6*\1 + cot (x)/*\1 + tan (x)/ - 4*\1 + cot (x)/*cot(x)*tan(x) - ------------------------------ - ----------------------- + ----------------------- + 4*tan (x)*\1 + tan (x)/*log(cot(x)) - ------------------------------------|
|\ cot(x) / \ cot(x) / | 2 cot(x) | 2 3 cot(x) cot(x) |
\ \ cot (x) / cot (x) cot (x) /
$$\left(4 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(\cot{\left(x \right)} \right)} \tan^{2}{\left(x \right)} + \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(\cot{\left(x \right)} \right)} - \frac{\left(\cot^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}}{\cot{\left(x \right)}}\right)^{3} + 2 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \log{\left(\cot{\left(x \right)} \right)} - 4 \left(\cot^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} \cot{\left(x \right)} - 3 \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(\cot{\left(x \right)} \right)} - \frac{\left(\cot^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}}{\cot{\left(x \right)}}\right) \left(- 2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(\cot{\left(x \right)} \right)} \tan{\left(x \right)} - 2 \left(\cot^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right) \left(\cot^{2}{\left(x \right)} + 1\right)}{\cot{\left(x \right)}} + \frac{\left(\cot^{2}{\left(x \right)} + 1\right)^{2} \tan{\left(x \right)}}{\cot^{2}{\left(x \right)}}\right) - \frac{6 \left(\tan^{2}{\left(x \right)} + 1\right) \left(\cot^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}}{\cot{\left(x \right)}} + 6 \left(\tan^{2}{\left(x \right)} + 1\right) \left(\cot^{2}{\left(x \right)} + 1\right) + \frac{4 \left(\cot^{2}{\left(x \right)} + 1\right)^{2} \tan{\left(x \right)}}{\cot{\left(x \right)}} - \frac{3 \left(\tan^{2}{\left(x \right)} + 1\right) \left(\cot^{2}{\left(x \right)} + 1\right)^{2}}{\cot^{2}{\left(x \right)}} - \frac{2 \left(\cot^{2}{\left(x \right)} + 1\right)^{3} \tan{\left(x \right)}}{\cot^{3}{\left(x \right)}}\right) \cot^{\tan{\left(x \right)}}{\left(x \right)}$$
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