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:
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Производная cos(x)-sqrt(3*sin(x))
- Производная (x-22)*e^x-21
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Производная 1+(sin(x))^2
- Производная -14*x+7*tan(x)+7*pi/2+11
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Идентичные выражения
- ((log(x)/log(два))*(x+ четыре))^(cot(семь *x))
- (( логарифм от (x) делить на логарифм от (2)) умножить на (x плюс 4)) в степени ( котангенс от (7 умножить на x))
- (( логарифм от (x) делить на логарифм от (два)) умножить на (x плюс четыре)) в степени ( котангенс от (семь умножить на x))
- ((log(x)/log(2))*(x+4))(cot(7*x))
- logx/log2*x+4cot7*x
- ((log(x)/log(2))(x+4))^(cot(7x))
- ((log(x)/log(2))(x+4))(cot(7x))
- logx/log2x+4cot7x
- logx/log2x+4^cot7x
- ((log(x) разделить на log(2))*(x+4))^(cot(7*x))
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Похожие выражения
- ((log(x)/log(2))*(x-4))^(cot(7*x))
Производная ((log(x)/log(2))*(x+4))^(cot(7*x))
Решение
Вы ввели
[src]
cot(7*x) /log(x)*(x + 4)\ |--------------| \ log(2) /
$$\left(\frac{\left(x + 4\right) \log{\left(x \right)}}{\log{\left(2 \right)}}\right)^{\cot{\left(7 x \right)}}$$
/ cot(7*x)\ d |/log(x)*(x + 4)\ | --||--------------| | dx\\ log(2) / /
$$\frac{d}{d x} \left(\frac{\left(x + 4\right) \log{\left(x \right)}}{\log{\left(2 \right)}}\right)^{\cot{\left(7 x \right)}}$$
Подробное решение
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Не могу найти шаги в поиске этой производной.
Но производная
Ответ:
Первая производная
[src]
/ /log(x) x + 4 \ \
cot(7*x) | |------ + --------|*cot(7*x)*log(2)|
/log(x)*(x + 4)\ |/ 2 \ /log(x)*(x + 4)\ \log(2) x*log(2)/ |
|--------------| *|\-7 - 7*cot (7*x)/*log|--------------| + -----------------------------------|
\ log(2) / \ \ log(2) / (x + 4)*log(x) /
$$\left(\frac{\left(x + 4\right) \log{\left(x \right)}}{\log{\left(2 \right)}}\right)^{\cot{\left(7 x \right)}} \left(\left(- 7 \cot^{2}{\left(7 x \right)} - 7\right) \log{\left(\frac{\left(x + 4\right) \log{\left(x \right)}}{\log{\left(2 \right)}} \right)} + \frac{\left(\frac{\log{\left(x \right)}}{\log{\left(2 \right)}} + \frac{x + 4}{x \log{\left(2 \right)}}\right) \log{\left(2 \right)} \cot{\left(7 x \right)}}{\left(x + 4\right) \log{\left(x \right)}}\right)$$
Вторая производная
[src]
/ 2 \
|/ /4 + x \ \ /4 + x \ / 2 \ /4 + x \ / 4 + x\ /4 + x \ |
cot(7*x) || |----- + log(x)|*cot(7*x)| |----- + log(x)|*cot(7*x) 14*\1 + cot (7*x)/*|----- + log(x)| |2 - -----|*cot(7*x) |----- + log(x)|*cot(7*x)|
/(4 + x)*log(x)\ || / 2 \ /(4 + x)*log(x)\ \ x / | / 2 \ /(4 + x)*log(x)\ \ x / \ x / \ x / \ x / |
|--------------| *||7*\1 + cot (7*x)/*log|--------------| - -------------------------| + 98*\1 + cot (7*x)/*cot(7*x)*log|--------------| - ------------------------- - ----------------------------------- + -------------------- - -------------------------|
\ log(2) / |\ \ log(2) / (4 + x)*log(x) / \ log(2) / 2 (4 + x)*log(x) x*(4 + x)*log(x) 2 |
\ (4 + x) *log(x) x*(4 + x)*log (x) /
$$\left(\frac{\left(x + 4\right) \log{\left(x \right)}}{\log{\left(2 \right)}}\right)^{\cot{\left(7 x \right)}} \left(98 \left(\cot^{2}{\left(7 x \right)} + 1\right) \log{\left(\frac{\left(x + 4\right) \log{\left(x \right)}}{\log{\left(2 \right)}} \right)} \cot{\left(7 x \right)} + \left(7 \left(\cot^{2}{\left(7 x \right)} + 1\right) \log{\left(\frac{\left(x + 4\right) \log{\left(x \right)}}{\log{\left(2 \right)}} \right)} - \frac{\left(\log{\left(x \right)} + \frac{x + 4}{x}\right) \cot{\left(7 x \right)}}{\left(x + 4\right) \log{\left(x \right)}}\right)^{2} - \frac{14 \left(\log{\left(x \right)} + \frac{x + 4}{x}\right) \left(\cot^{2}{\left(7 x \right)} + 1\right)}{\left(x + 4\right) \log{\left(x \right)}} - \frac{\left(\log{\left(x \right)} + \frac{x + 4}{x}\right) \cot{\left(7 x \right)}}{\left(x + 4\right)^{2} \log{\left(x \right)}} + \frac{\left(2 - \frac{x + 4}{x}\right) \cot{\left(7 x \right)}}{x \left(x + 4\right) \log{\left(x \right)}} - \frac{\left(\log{\left(x \right)} + \frac{x + 4}{x}\right) \cot{\left(7 x \right)}}{x \left(x + 4\right) \log{\left(x \right)}^{2}}\right)$$
Третья производная
[src]
/ 3 \
| / /4 + x \ \ / /4 + x \ \ / /4 + x \ / 2 \ /4 + x \ /4 + x \ / 4 + x\ \ /4 + x \ / 2 \ /4 + x \ /4 + x \ / 2*(4 + x)\ / 2 \ / 4 + x\ / 4 + x\ / 4 + x\ /4 + x \ /4 + x \ / 2 \ /4 + x \ / 2 \ /4 + x \ |
cot(7*x) | | |----- + log(x)|*cot(7*x)| 2 | |----- + log(x)|*cot(7*x)| | |----- + log(x)|*cot(7*x) 14*\1 + cot (7*x)/*|----- + log(x)| |----- + log(x)|*cot(7*x) |2 - -----|*cot(7*x)| 2*|----- + log(x)|*cot(7*x) 21*\1 + cot (7*x)/*|----- + log(x)| |----- + log(x)|*cot(7*x) |3 - ---------|*cot(7*x) 21*\1 + cot (7*x)/*|2 - -----| 2*|2 - -----|*cot(7*x) 2*|2 - -----|*cot(7*x) 2*|----- + log(x)|*cot(7*x) 2*|----- + log(x)|*cot(7*x) 21*\1 + cot (7*x)/*|----- + log(x)| 294*\1 + cot (7*x)/*|----- + log(x)|*cot(7*x)|
/(4 + x)*log(x)\ | | / 2 \ /(4 + x)*log(x)\ \ x / | / 2 \ /(4 + x)*log(x)\ | / 2 \ /(4 + x)*log(x)\ \ x / | | / 2 \ /(4 + x)*log(x)\ \ x / \ x / \ x / \ x / | 2 / 2 \ /(4 + x)*log(x)\ \ x / \ x / \ x / \ x / \ x / \ x / \ x / \ x / \ x / \ x / \ x / |
|--------------| *|- |7*\1 + cot (7*x)/*log|--------------| - -------------------------| - 686*\1 + cot (7*x)/ *log|--------------| + 3*|7*\1 + cot (7*x)/*log|--------------| - -------------------------|*|- 98*\1 + cot (7*x)/*cot(7*x)*log|--------------| + ------------------------- + ----------------------------------- + ------------------------- - --------------------| - 1372*cot (7*x)*\1 + cot (7*x)/*log|--------------| + --------------------------- + ----------------------------------- + ------------------------- - ------------------------ - ------------------------------ - ---------------------- - ---------------------- + --------------------------- + --------------------------- + ----------------------------------- + ---------------------------------------------|
\ log(2) / | \ \ log(2) / (4 + x)*log(x) / \ log(2) / \ \ log(2) / (4 + x)*log(x) / | \ log(2) / 2 (4 + x)*log(x) 2 x*(4 + x)*log(x) | \ log(2) / 3 2 2 2 2 x*(4 + x)*log(x) 2 2 2 2 2 2 3 2 (4 + x)*log(x) |
\ \ (4 + x) *log(x) x*(4 + x)*log (x) / (4 + x) *log(x) (4 + x) *log(x) x *(4 + x)*log (x) x *(4 + x)*log(x) x*(4 + x) *log(x) x *(4 + x)*log (x) x*(4 + x) *log (x) x *(4 + x)*log (x) x*(4 + x)*log (x) /
$$\left(\frac{\left(x + 4\right) \log{\left(x \right)}}{\log{\left(2 \right)}}\right)^{\cot{\left(7 x \right)}} \left(- 1372 \left(\cot^{2}{\left(7 x \right)} + 1\right) \log{\left(\frac{\left(x + 4\right) \log{\left(x \right)}}{\log{\left(2 \right)}} \right)} \cot^{2}{\left(7 x \right)} - \left(7 \left(\cot^{2}{\left(7 x \right)} + 1\right) \log{\left(\frac{\left(x + 4\right) \log{\left(x \right)}}{\log{\left(2 \right)}} \right)} - \frac{\left(\log{\left(x \right)} + \frac{x + 4}{x}\right) \cot{\left(7 x \right)}}{\left(x + 4\right) \log{\left(x \right)}}\right)^{3} - 686 \left(\cot^{2}{\left(7 x \right)} + 1\right)^{2} \log{\left(\frac{\left(x + 4\right) \log{\left(x \right)}}{\log{\left(2 \right)}} \right)} + 3 \cdot \left(7 \left(\cot^{2}{\left(7 x \right)} + 1\right) \log{\left(\frac{\left(x + 4\right) \log{\left(x \right)}}{\log{\left(2 \right)}} \right)} - \frac{\left(\log{\left(x \right)} + \frac{x + 4}{x}\right) \cot{\left(7 x \right)}}{\left(x + 4\right) \log{\left(x \right)}}\right) \left(- 98 \left(\cot^{2}{\left(7 x \right)} + 1\right) \log{\left(\frac{\left(x + 4\right) \log{\left(x \right)}}{\log{\left(2 \right)}} \right)} \cot{\left(7 x \right)} + \frac{14 \left(\log{\left(x \right)} + \frac{x + 4}{x}\right) \left(\cot^{2}{\left(7 x \right)} + 1\right)}{\left(x + 4\right) \log{\left(x \right)}} + \frac{\left(\log{\left(x \right)} + \frac{x + 4}{x}\right) \cot{\left(7 x \right)}}{\left(x + 4\right)^{2} \log{\left(x \right)}} - \frac{\left(2 - \frac{x + 4}{x}\right) \cot{\left(7 x \right)}}{x \left(x + 4\right) \log{\left(x \right)}} + \frac{\left(\log{\left(x \right)} + \frac{x + 4}{x}\right) \cot{\left(7 x \right)}}{x \left(x + 4\right) \log{\left(x \right)}^{2}}\right) + \frac{294 \left(\log{\left(x \right)} + \frac{x + 4}{x}\right) \left(\cot^{2}{\left(7 x \right)} + 1\right) \cot{\left(7 x \right)}}{\left(x + 4\right) \log{\left(x \right)}} + \frac{21 \left(\log{\left(x \right)} + \frac{x + 4}{x}\right) \left(\cot^{2}{\left(7 x \right)} + 1\right)}{\left(x + 4\right)^{2} \log{\left(x \right)}} - \frac{21 \cdot \left(2 - \frac{x + 4}{x}\right) \left(\cot^{2}{\left(7 x \right)} + 1\right)}{x \left(x + 4\right) \log{\left(x \right)}} + \frac{2 \left(\log{\left(x \right)} + \frac{x + 4}{x}\right) \cot{\left(7 x \right)}}{\left(x + 4\right)^{3} \log{\left(x \right)}} - \frac{2 \cdot \left(2 - \frac{x + 4}{x}\right) \cot{\left(7 x \right)}}{x \left(x + 4\right)^{2} \log{\left(x \right)}} + \frac{21 \left(\log{\left(x \right)} + \frac{x + 4}{x}\right) \left(\cot^{2}{\left(7 x \right)} + 1\right)}{x \left(x + 4\right) \log{\left(x \right)}^{2}} - \frac{\left(3 - \frac{2 \left(x + 4\right)}{x}\right) \cot{\left(7 x \right)}}{x^{2} \left(x + 4\right) \log{\left(x \right)}} + \frac{2 \left(\log{\left(x \right)} + \frac{x + 4}{x}\right) \cot{\left(7 x \right)}}{x \left(x + 4\right)^{2} \log{\left(x \right)}^{2}} - \frac{2 \cdot \left(2 - \frac{x + 4}{x}\right) \cot{\left(7 x \right)}}{x^{2} \left(x + 4\right) \log{\left(x \right)}^{2}} + \frac{\left(\log{\left(x \right)} + \frac{x + 4}{x}\right) \cot{\left(7 x \right)}}{x^{2} \left(x + 4\right) \log{\left(x \right)}^{2}} + \frac{2 \left(\log{\left(x \right)} + \frac{x + 4}{x}\right) \cot{\left(7 x \right)}}{x^{2} \left(x + 4\right) \log{\left(x \right)}^{3}}\right)$$
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