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^2*log(x)
- Производная sqrt(x+4)
- Производная cot(pi*x/2)
- Производная 2^x-1
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Идентичные выражения
- (cos(три *x)- один -(девять *x^ два)/ два)/(x^ четыре *sinh(девять / четыре *x))*x^ три
- ( косинус от (3 умножить на x) минус 1 минус (9 умножить на x в квадрате ) делить на 2) делить на (x в степени 4 умножить на гиперболический синус от (9 делить на 4 умножить на x)) умножить на x в кубе
- ( косинус от (три умножить на x) минус один минус (девять умножить на x в степени два) делить на два) делить на (x в степени четыре умножить на гиперболический синус от (девять делить на четыре умножить на x)) умножить на x в степени три
- (cos(3*x)-1-(9*x2)/2)/(x4*sinh(9/4*x))*x3
- cos3*x-1-9*x2/2/x4*sinh9/4*x*x3
- (cos(3*x)-1-(9*x²)/2)/(x⁴*sinh(9/4*x))*x³
- (cos(3*x)-1-(9*x в степени 2)/2)/(x в степени 4*sinh(9/4*x))*x в степени 3
- (cos(3x)-1-(9x^2)/2)/(x^4sinh(9/4x))x^3
- (cos(3x)-1-(9x2)/2)/(x4sinh(9/4x))x3
- cos3x-1-9x2/2/x4sinh9/4xx3
- cos3x-1-9x^2/2/x^4sinh9/4xx^3
- (cos(3*x)-1-(9*x^2) разделить на 2) разделить на (x^4*sinh(9 разделить на 4*x))*x^3
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Похожие выражения
- (cos(3*x)+1-(9*x^2)/2)/(x^4*sinh(9/4*x))*x^3
- (cos(3*x)-1+(9*x^2)/2)/(x^4*sinh(9/4*x))*x^3
Производная (cos(3*x)-1-(9*x^2)/2)/(x^4*sinh(9/4*x))*x^3
Решение
Вы ввели
[src]
/ 2\
| 9*x | 3
|cos(3*x) - 1 - ----|*x
\ 2 /
------------------------
4 /9*x\
x *sinh|---|
\ 4 /
$$\frac{x^{3} \left(- \frac{9 x^{2}}{2} + \cos{\left(3 x \right)} - 1\right)}{x^{4} \sinh{\left(\frac{9 x}{4} \right)}}$$
// 2\ \ || 9*x | 3| ||cos(3*x) - 1 - ----|*x | d |\ 2 / | --|------------------------| dx| 4 /9*x\ | | x *sinh|---| | \ \ 4 / /
$$\frac{d}{d x} \frac{x^{3} \left(- \frac{9 x^{2}}{2} + \cos{\left(3 x \right)} - 1\right)}{x^{4} \sinh{\left(\frac{9 x}{4} \right)}}$$
Первая производная
[src]
/ 4 /9*x\\
| 9*x *cosh|---|| / 2\
| 3 /9*x\ \ 4 /| | 9*x |
/ 2\ |- 4*x *sinh|---| - --------------|*|cos(3*x) - 1 - ----|
3 1 2 1 | 9*x | \ \ 4 / 4 / \ 2 /
x *------------*(-9*x - 3*sin(3*x)) + 3*x *------------*|cos(3*x) - 1 - ----| + ---------------------------------------------------------
4 /9*x\ 4 /9*x\ \ 2 / 5 2/9*x\
x *sinh|---| x *sinh|---| x *sinh |---|
\ 4 / \ 4 / \ 4 /
$$x^{3} \cdot \frac{1}{x^{4} \sinh{\left(\frac{9 x}{4} \right)}} \left(- 9 x - 3 \sin{\left(3 x \right)}\right) + 3 x^{2} \cdot \frac{1}{x^{4} \sinh{\left(\frac{9 x}{4} \right)}} \left(- \frac{9 x^{2}}{2} + \cos{\left(3 x \right)} - 1\right) + \frac{\left(- \frac{9 x^{4} \cosh{\left(\frac{9 x}{4} \right)}}{4} - 4 x^{3} \sinh{\left(\frac{9 x}{4} \right)}\right) \left(- \frac{9 x^{2}}{2} + \cos{\left(3 x \right)} - 1\right)}{x^{5} \sinh^{2}{\left(\frac{9 x}{4} \right)}}$$
Вторая производная
[src]
// /9*x\\ / /9*x\ 2 /9*x\ /9*x\\ / /9*x\ /9*x\\ / /9*x\ /9*x\\ /9*x\\
|| 9*cosh|---|| 3*|64*sinh|---| + 27*x *sinh|---| + 96*x*cosh|---|| 16*|16*sinh|---| + 9*x*cosh|---|| 9*|16*sinh|---| + 9*x*cosh|---||*cosh|---||
/ 2\ ||16 \ 4 /| / /9*x\ /9*x\\ \ \ 4 / \ 4 / \ 4 // \ \ 4 / \ 4 // \ \ 4 / \ 4 // \ 4 /|
\2 - 2*cos(3*x) + 9*x /*||-- + -----------|*|16*sinh|---| + 9*x*cosh|---|| - --------------------------------------------------- + --------------------------------- + ------------------------------------------|
||x /9*x\ | \ \ 4 / \ 4 // x x /9*x\ | / /9*x\ /9*x\\ / /9*x\ /9*x\\ / 2\
/ 2\ || sinh|---| | sinh|---| | 3*(3*x + sin(3*x))*|16*sinh|---| + 9*x*cosh|---|| 3*|16*sinh|---| + 9*x*cosh|---||*\2 - 2*cos(3*x) + 9*x /
18*(3*x + sin(3*x)) 3*\2 - 2*cos(3*x) + 9*x / \\ \ 4 / / \ 4 / / \ \ 4 / \ 4 // \ \ 4 / \ 4 //
-9 - 9*cos(3*x) - ------------------- - ------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + ------------------------------------------------- + --------------------------------------------------------
x 2 /9*x\ /9*x\ 2 /9*x\
x 32*x*sinh|---| 2*x*sinh|---| 4*x *sinh|---|
\ 4 / \ 4 / \ 4 /
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
/9*x\
x*sinh|---|
\ 4 /
$$\frac{- 9 \cos{\left(3 x \right)} - 9 + \frac{3 \cdot \left(3 x + \sin{\left(3 x \right)}\right) \left(9 x \cosh{\left(\frac{9 x}{4} \right)} + 16 \sinh{\left(\frac{9 x}{4} \right)}\right)}{2 x \sinh{\left(\frac{9 x}{4} \right)}} - \frac{18 \cdot \left(3 x + \sin{\left(3 x \right)}\right)}{x} - \frac{\left(9 x^{2} - 2 \cos{\left(3 x \right)} + 2\right) \left(\left(9 x \cosh{\left(\frac{9 x}{4} \right)} + 16 \sinh{\left(\frac{9 x}{4} \right)}\right) \left(\frac{9 \cosh{\left(\frac{9 x}{4} \right)}}{\sinh{\left(\frac{9 x}{4} \right)}} + \frac{16}{x}\right) + \frac{9 \cdot \left(9 x \cosh{\left(\frac{9 x}{4} \right)} + 16 \sinh{\left(\frac{9 x}{4} \right)}\right) \cosh{\left(\frac{9 x}{4} \right)}}{\sinh{\left(\frac{9 x}{4} \right)}} + \frac{16 \cdot \left(9 x \cosh{\left(\frac{9 x}{4} \right)} + 16 \sinh{\left(\frac{9 x}{4} \right)}\right)}{x} - \frac{3 \cdot \left(27 x^{2} \sinh{\left(\frac{9 x}{4} \right)} + 96 x \cosh{\left(\frac{9 x}{4} \right)} + 64 \sinh{\left(\frac{9 x}{4} \right)}\right)}{x}\right)}{32 x \sinh{\left(\frac{9 x}{4} \right)}} + \frac{3 \cdot \left(9 x \cosh{\left(\frac{9 x}{4} \right)} + 16 \sinh{\left(\frac{9 x}{4} \right)}\right) \left(9 x^{2} - 2 \cos{\left(3 x \right)} + 2\right)}{4 x^{2} \sinh{\left(\frac{9 x}{4} \right)}} - \frac{3 \cdot \left(9 x^{2} - 2 \cos{\left(3 x \right)} + 2\right)}{x^{2}}}{x \sinh{\left(\frac{9 x}{4} \right)}}$$
Третья производная
[src]
/ / /9*x\\ / /9*x\\ / /9*x\\ \
| | 9*cosh|---|| | 9*cosh|---|| | 9*cosh|---|| |
| |16 \ 4 /| / /9*x\ 2 /9*x\ /9*x\\ |16 \ 4 /| / /9*x\ /9*x\\ |16 \ 4 /| / /9*x\ /9*x\\ /9*x\ |
| 3*|-- + -----------|*|64*sinh|---| + 27*x *sinh|---| + 96*x*cosh|---|| 16*|-- + -----------|*|16*sinh|---| + 9*x*cosh|---|| 9*|-- + -----------|*|16*sinh|---| + 9*x*cosh|---||*cosh|---| |
// /9*x\\ / /9*x\ 2 /9*x\ /9*x\\ / /9*x\ /9*x\\ / /9*x\ /9*x\\ /9*x\\ // /9*x\\ / /9*x\ 2 /9*x\ /9*x\\ / /9*x\ /9*x\\ / /9*x\ /9*x\\ /9*x\\ | / 2/9*x\ /9*x\\ / /9*x\ 2 /9*x\ /9*x\\ / /9*x\ 3 /9*x\ 2 /9*x\ /9*x\\ / /9*x\ /9*x\\ |x /9*x\ | \ \ 4 / \ 4 / \ 4 // |x /9*x\ | \ \ 4 / \ 4 // 2/9*x\ / /9*x\ /9*x\\ / /9*x\ 2 /9*x\ /9*x\\ /9*x\ |x /9*x\ | \ \ 4 / \ 4 // \ 4 / / /9*x\ /9*x\\ /9*x\|
|| 9*cosh|---|| 3*|64*sinh|---| + 27*x *sinh|---| + 96*x*cosh|---|| 16*|16*sinh|---| + 9*x*cosh|---|| 9*|16*sinh|---| + 9*x*cosh|---||*cosh|---|| || 9*cosh|---|| 3*|64*sinh|---| + 27*x *sinh|---| + 96*x*cosh|---|| 16*|16*sinh|---| + 9*x*cosh|---|| 9*|16*sinh|---| + 9*x*cosh|---||*cosh|---|| | | 162*cosh |---| 288*cosh|---|| 144*|64*sinh|---| + 27*x *sinh|---| + 96*x*cosh|---|| 3*|512*sinh|---| + 243*x *cosh|---| + 1296*x *sinh|---| + 1728*x*cosh|---|| 576*|16*sinh|---| + 9*x*cosh|---|| | sinh|---| | | sinh|---| | 243*cosh |---|*|16*sinh|---| + 9*x*cosh|---|| 81*|64*sinh|---| + 27*x *sinh|---| + 96*x*cosh|---||*cosh|---| | sinh|---| | 576*|16*sinh|---| + 9*x*cosh|---||*cosh|---||
||16 \ 4 /| / /9*x\ /9*x\\ \ \ 4 / \ 4 / \ 4 // \ \ 4 / \ 4 // \ \ 4 / \ 4 // \ 4 /| / 2\ ||16 \ 4 /| / /9*x\ /9*x\\ \ \ 4 / \ 4 / \ 4 // \ \ 4 / \ 4 // \ \ 4 / \ 4 // \ 4 /| / 2\ | /9*x\ / /9*x\ /9*x\\ | 320 \ 4 / \ 4 /| /9*x\ \ \ 4 / \ 4 / \ 4 // \ \ 4 / \ 4 / \ 4 / \ 4 // \ \ 4 / \ 4 // \ \ 4 / / \ \ 4 / / \ 4 / \ \ 4 / \ 4 // \ \ 4 / \ 4 / \ 4 // \ 4 / \ \ 4 / / \ \ 4 / \ 4 // \ 4 /|
9*(3*x + sin(3*x))*||-- + -----------|*|16*sinh|---| + 9*x*cosh|---|| - --------------------------------------------------- + --------------------------------- + ------------------------------------------| 9*\2 - 2*cos(3*x) + 9*x /*||-- + -----------|*|16*sinh|---| + 9*x*cosh|---|| - --------------------------------------------------- + --------------------------------- + ------------------------------------------| \2 - 2*cos(3*x) + 9*x /*|- 1296*sinh|---| + |16*sinh|---| + 9*x*cosh|---||*|-81 + --- + -------------- + -------------| - 729*x*cosh|---| - ----------------------------------------------------- + --------------------------------------------------------------------------- + ---------------------------------- - ---------------------------------------------------------------------- + ---------------------------------------------------- + --------------------------------------------- - -------------------------------------------------------------- + ------------------------------------------------------------- + --------------------------------------------|
||x /9*x\ | \ \ 4 / \ 4 // x x /9*x\ | ||x /9*x\ | \ \ 4 / \ 4 // x x /9*x\ | | \ 4 / \ \ 4 / \ 4 // | 2 2/9*x\ /9*x\ | \ 4 / 2 2 2 x x 2/9*x\ /9*x\ /9*x\ /9*x\ | / /9*x\ /9*x\\ / 2\ / /9*x\ /9*x\\ / /9*x\ /9*x\\
/ 2\ || sinh|---| | sinh|---| | || sinh|---| | sinh|---| | | | x sinh |---| x*sinh|---| | x x x sinh |---| x*sinh|---| sinh|---| x*sinh|---| | 9*|16*sinh|---| + 9*x*cosh|---||*\2 - 2*cos(3*x) + 9*x / 27*(3*x + sin(3*x))*|16*sinh|---| + 9*x*cosh|---|| 27*(1 + cos(3*x))*|16*sinh|---| + 9*x*cosh|---||
81*(1 + cos(3*x)) 54*(3*x + sin(3*x)) 3*\2 - 2*cos(3*x) + 9*x / \\ \ 4 / / \ 4 / / \\ \ 4 / / \ 4 / / \ \ \ 4 / \ 4 / / \ 4 / \ 4 / \ 4 / \ 4 / / \ \ 4 / \ 4 // \ \ 4 / \ 4 // \ \ 4 / \ 4 //
27*sin(3*x) - ----------------- - ------------------- - ------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------- + -------------------------------------------------- + ------------------------------------------------
x 2 3 /9*x\ 2 /9*x\ /9*x\ 3 /9*x\ 2 /9*x\ /9*x\
x x 16*x*sinh|---| 32*x *sinh|---| 128*x*sinh|---| 4*x *sinh|---| 2*x *sinh|---| 4*x*sinh|---|
\ 4 / \ 4 / \ 4 / \ 4 / \ 4 / \ 4 /
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
/9*x\
x*sinh|---|
\ 4 /
$$\frac{27 \sin{\left(3 x \right)} - \frac{9 \cdot \left(3 x + \sin{\left(3 x \right)}\right) \left(\left(9 x \cosh{\left(\frac{9 x}{4} \right)} + 16 \sinh{\left(\frac{9 x}{4} \right)}\right) \left(\frac{9 \cosh{\left(\frac{9 x}{4} \right)}}{\sinh{\left(\frac{9 x}{4} \right)}} + \frac{16}{x}\right) + \frac{9 \cdot \left(9 x \cosh{\left(\frac{9 x}{4} \right)} + 16 \sinh{\left(\frac{9 x}{4} \right)}\right) \cosh{\left(\frac{9 x}{4} \right)}}{\sinh{\left(\frac{9 x}{4} \right)}} + \frac{16 \cdot \left(9 x \cosh{\left(\frac{9 x}{4} \right)} + 16 \sinh{\left(\frac{9 x}{4} \right)}\right)}{x} - \frac{3 \cdot \left(27 x^{2} \sinh{\left(\frac{9 x}{4} \right)} + 96 x \cosh{\left(\frac{9 x}{4} \right)} + 64 \sinh{\left(\frac{9 x}{4} \right)}\right)}{x}\right)}{16 x \sinh{\left(\frac{9 x}{4} \right)}} + \frac{27 \cdot \left(9 x \cosh{\left(\frac{9 x}{4} \right)} + 16 \sinh{\left(\frac{9 x}{4} \right)}\right) \left(\cos{\left(3 x \right)} + 1\right)}{4 x \sinh{\left(\frac{9 x}{4} \right)}} - \frac{81 \left(\cos{\left(3 x \right)} + 1\right)}{x} + \frac{\left(9 x^{2} - 2 \cos{\left(3 x \right)} + 2\right) \left(- 729 x \cosh{\left(\frac{9 x}{4} \right)} + \frac{9 \cdot \left(9 x \cosh{\left(\frac{9 x}{4} \right)} + 16 \sinh{\left(\frac{9 x}{4} \right)}\right) \left(\frac{9 \cosh{\left(\frac{9 x}{4} \right)}}{\sinh{\left(\frac{9 x}{4} \right)}} + \frac{16}{x}\right) \cosh{\left(\frac{9 x}{4} \right)}}{\sinh{\left(\frac{9 x}{4} \right)}} + \left(9 x \cosh{\left(\frac{9 x}{4} \right)} + 16 \sinh{\left(\frac{9 x}{4} \right)}\right) \left(-81 + \frac{162 \cosh^{2}{\left(\frac{9 x}{4} \right)}}{\sinh^{2}{\left(\frac{9 x}{4} \right)}} + \frac{288 \cosh{\left(\frac{9 x}{4} \right)}}{x \sinh{\left(\frac{9 x}{4} \right)}} + \frac{320}{x^{2}}\right) + \frac{243 \cdot \left(9 x \cosh{\left(\frac{9 x}{4} \right)} + 16 \sinh{\left(\frac{9 x}{4} \right)}\right) \cosh^{2}{\left(\frac{9 x}{4} \right)}}{\sinh^{2}{\left(\frac{9 x}{4} \right)}} - 1296 \sinh{\left(\frac{9 x}{4} \right)} + \frac{16 \cdot \left(9 x \cosh{\left(\frac{9 x}{4} \right)} + 16 \sinh{\left(\frac{9 x}{4} \right)}\right) \left(\frac{9 \cosh{\left(\frac{9 x}{4} \right)}}{\sinh{\left(\frac{9 x}{4} \right)}} + \frac{16}{x}\right)}{x} - \frac{3 \cdot \left(\frac{9 \cosh{\left(\frac{9 x}{4} \right)}}{\sinh{\left(\frac{9 x}{4} \right)}} + \frac{16}{x}\right) \left(27 x^{2} \sinh{\left(\frac{9 x}{4} \right)} + 96 x \cosh{\left(\frac{9 x}{4} \right)} + 64 \sinh{\left(\frac{9 x}{4} \right)}\right)}{x} + \frac{576 \cdot \left(9 x \cosh{\left(\frac{9 x}{4} \right)} + 16 \sinh{\left(\frac{9 x}{4} \right)}\right) \cosh{\left(\frac{9 x}{4} \right)}}{x \sinh{\left(\frac{9 x}{4} \right)}} - \frac{81 \cdot \left(27 x^{2} \sinh{\left(\frac{9 x}{4} \right)} + 96 x \cosh{\left(\frac{9 x}{4} \right)} + 64 \sinh{\left(\frac{9 x}{4} \right)}\right) \cosh{\left(\frac{9 x}{4} \right)}}{x \sinh{\left(\frac{9 x}{4} \right)}} + \frac{576 \cdot \left(9 x \cosh{\left(\frac{9 x}{4} \right)} + 16 \sinh{\left(\frac{9 x}{4} \right)}\right)}{x^{2}} - \frac{144 \cdot \left(27 x^{2} \sinh{\left(\frac{9 x}{4} \right)} + 96 x \cosh{\left(\frac{9 x}{4} \right)} + 64 \sinh{\left(\frac{9 x}{4} \right)}\right)}{x^{2}} + \frac{3 \cdot \left(243 x^{3} \cosh{\left(\frac{9 x}{4} \right)} + 1296 x^{2} \sinh{\left(\frac{9 x}{4} \right)} + 1728 x \cosh{\left(\frac{9 x}{4} \right)} + 512 \sinh{\left(\frac{9 x}{4} \right)}\right)}{x^{2}}\right)}{128 x \sinh{\left(\frac{9 x}{4} \right)}} + \frac{27 \cdot \left(3 x + \sin{\left(3 x \right)}\right) \left(9 x \cosh{\left(\frac{9 x}{4} \right)} + 16 \sinh{\left(\frac{9 x}{4} \right)}\right)}{2 x^{2} \sinh{\left(\frac{9 x}{4} \right)}} - \frac{54 \cdot \left(3 x + \sin{\left(3 x \right)}\right)}{x^{2}} - \frac{9 \cdot \left(9 x^{2} - 2 \cos{\left(3 x \right)} + 2\right) \left(\left(9 x \cosh{\left(\frac{9 x}{4} \right)} + 16 \sinh{\left(\frac{9 x}{4} \right)}\right) \left(\frac{9 \cosh{\left(\frac{9 x}{4} \right)}}{\sinh{\left(\frac{9 x}{4} \right)}} + \frac{16}{x}\right) + \frac{9 \cdot \left(9 x \cosh{\left(\frac{9 x}{4} \right)} + 16 \sinh{\left(\frac{9 x}{4} \right)}\right) \cosh{\left(\frac{9 x}{4} \right)}}{\sinh{\left(\frac{9 x}{4} \right)}} + \frac{16 \cdot \left(9 x \cosh{\left(\frac{9 x}{4} \right)} + 16 \sinh{\left(\frac{9 x}{4} \right)}\right)}{x} - \frac{3 \cdot \left(27 x^{2} \sinh{\left(\frac{9 x}{4} \right)} + 96 x \cosh{\left(\frac{9 x}{4} \right)} + 64 \sinh{\left(\frac{9 x}{4} \right)}\right)}{x}\right)}{32 x^{2} \sinh{\left(\frac{9 x}{4} \right)}} + \frac{9 \cdot \left(9 x \cosh{\left(\frac{9 x}{4} \right)} + 16 \sinh{\left(\frac{9 x}{4} \right)}\right) \left(9 x^{2} - 2 \cos{\left(3 x \right)} + 2\right)}{4 x^{3} \sinh{\left(\frac{9 x}{4} \right)}} - \frac{3 \cdot \left(9 x^{2} - 2 \cos{\left(3 x \right)} + 2\right)}{x^{3}}}{x \sinh{\left(\frac{9 x}{4} \right)}}$$
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