Sr Examen
Otras calculadoras
- Derivada de una función implícitamente dada
- Derivada de una función paramétrica
- Derivada parcial de la función
- Análisis de la función gráfica
- Integrales paso a paso
- Ecuaciones diferenciales paso a paso
- Límites paso por paso
-
¿Cómo usar?
- Derivada de:
-
Derivada de -2x
-
Derivada de 1/x^5
-
Derivada de e^-1
-
Derivada de x^2sinx
-
Expresiones idénticas
- x*tanh(x/(x*sin(x^(exp(sinh(x))))))/(log(x^exp(x))+log(cos(x)/sin(x)))
- x multiplicar por tangente de gente hiperbólica de (x dividir por (x multiplicar por seno de (x en el grado ( exponente de ( seno hiperbólico de (x)))))) dividir por ( logaritmo de (x en el grado exponente de (x)) más logaritmo de ( coseno de (x) dividir por seno de (x)))
- x*tanh(x/(x*sin(x(exp(sinh(x))))))/(log(xexp(x))+log(cos(x)/sin(x)))
- x*tanhx/x*sinxexpsinhx/logxexpx+logcosx/sinx
- xtanh(x/(xsin(x^(exp(sinh(x))))))/(log(x^exp(x))+log(cos(x)/sin(x)))
- xtanh(x/(xsin(x(exp(sinh(x))))))/(log(xexp(x))+log(cos(x)/sin(x)))
- xtanhx/xsinxexpsinhx/logxexpx+logcosx/sinx
- xtanhx/xsinx^expsinhx/logx^expx+logcosx/sinx
- x*tanh(x dividir por (x*sin(x^(exp(sinh(x)))))) dividir por (log(x^exp(x))+log(cos(x) dividir por sin(x)))
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Expresiones semejantes
- x*tanh(x/(x*sin(x^(exp(sinh(x))))))/(log(x^exp(x))-log(cos(x)/sin(x)))
- x*tanh(x/(x*sin(x^(exp(sinh(x))))))/(log(x^exp(x))+log(cosx/sinx))
-
Expresiones con funciones
- Seno sin
- sin(5-3*x)
- sin(x/5)
- sin²(x)
- sin(x)/3
- sin(x-(3/5))-(8/5)
- Exponente exp
- exp(8*x)
- exp(x^1/2)
- exp(y)
- Logaritmo log
- loga
- log(2)*x
- log(sin(2*x))
- loga^x
- log((x-1)/(x+1))
- Exponente exp
- exp(8*x)
- exp(x^1/2)
- exp(y)
- Logaritmo log
- loga
- log(2)*x
- log(sin(2*x))
- loga^x
- log((x-1)/(x+1))
- Coseno cos
- cos(3)^(2)*x
- cos^2(x^2)
- cos/sin
- cosx-sinx
- cosx^(sinx)
- Seno sin
- sin(5-3*x)
- sin(x/5)
- sin²(x)
- sin(x)/3
- sin(x-(3/5))-(8/5)
Derivada de x*tanh(x/(x*sin(x^(exp(sinh(x))))))/(log(x^exp(x))+log(cos(x)/sin(x)))
Solución
Ha introducido
[src]
/ x \
x*tanh|------------------|
| / / sinh(x)\\|
| | \e /||
\x*sin\x //
--------------------------
/ / x\\
| \e /| /cos(x)\
log\x / + log|------|
\sin(x)/
$$\frac{x \tanh{\left(\frac{x}{x \sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}} \right)}}{\log{\left(x^{e^{x}} \right)} + \log{\left(\frac{\cos{\left(x \right)}}{\sin{\left(x \right)}} \right)}}$$
(x*tanh(x/((x*sin(x^exp(sinh(x)))))))/(log(x^exp(x)) + log(cos(x)/sin(x)))
Primera derivada
[src]
/ / 2 \ \
/ / / sinh(x)\\ / sinh(x)\ / sinh(x) \ / / sinh(x)\\\ | | cos (x)| |
| | \e /| \e / |e sinh(x) | | \e /|| | |-1 - -------|*sin(x)|
| - sin\x / - x*x *|-------- + cosh(x)*e *log(x)|*cos\x /| | x | 2 | |
/ 2/ x \\ | 1 \ x / | / x \ | e x \ sin (x)/ | / x \
x*|1 - tanh |------------------||*|------------------ + ----------------------------------------------------------------------------------------| + tanh|------------------| x*|- -- - e *log(x) - ---------------------|*tanh|------------------|
| | / / sinh(x)\\|| | / / sinh(x)\\ / / sinh(x)\\ | | / / sinh(x)\\| \ x cos(x) / | / / sinh(x)\\|
| | | \e /||| | | \e /| 2| \e /| | | | \e /|| | | \e /||
\ \x*sin\x /// \x*sin\x / x*sin \x / / \x*sin\x // \x*sin\x //
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------
/ / x\\ 2
| \e /| /cos(x)\ / / / x\\ \
log\x / + log|------| | | \e /| /cos(x)\|
\sin(x)/ |log\x / + log|------||
\ \sin(x)//
$$\frac{x \left(- \frac{\left(-1 - \frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) \sin{\left(x \right)}}{\cos{\left(x \right)}} - e^{x} \log{\left(x \right)} - \frac{e^{x}}{x}\right) \tanh{\left(\frac{x}{x \sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}} \right)}}{\left(\log{\left(x^{e^{x}} \right)} + \log{\left(\frac{\cos{\left(x \right)}}{\sin{\left(x \right)}} \right)}\right)^{2}} + \frac{x \left(1 - \tanh^{2}{\left(\frac{x}{x \sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}} \right)}\right) \left(\frac{1}{x \sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}} + \frac{- x x^{e^{\sinh{\left(x \right)}}} \left(e^{\sinh{\left(x \right)}} \log{\left(x \right)} \cosh{\left(x \right)} + \frac{e^{\sinh{\left(x \right)}}}{x}\right) \cos{\left(x^{e^{\sinh{\left(x \right)}}} \right)} - \sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}}{x \sin^{2}{\left(x^{e^{\sinh{\left(x \right)}}} \right)}}\right) + \tanh{\left(\frac{x}{x \sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}} \right)}}{\log{\left(x^{e^{x}} \right)} + \log{\left(\frac{\cos{\left(x \right)}}{\sin{\left(x \right)}} \right)}}$$
Segunda derivada
[src]
/ 2 \
| / / sinh(x)\ / / sinh(x)\\ / / sinh(x)\\\ |
| | \e / /1 \ | \e /| sinh(x) | \e /|| |
| | x*x *|- + cosh(x)*log(x)|*cos\x /*e + sin\x /| |
| | \x / | / 1 \ | / 2 \
| / / / sinh(x)\ / / sinh(x)\\ / / sinh(x)\\\ / / sinh(x)\\ \ 2*|-1 + -------------------------------------------------------------------------------| *tanh|----------------| / / sinh(x)\ / / sinh(x)\\ / / sinh(x)\\\| / / / sinh(x)\ / / sinh(x)\\ / / sinh(x)\\\ \ | / / 2 \ \ |
| | /1 \ | \e / /1 \ | \e /| sinh(x) | \e /|| | \e /| | | / / sinh(x)\\ | | / / sinh(x)\\| | \e / /1 \ | \e /| sinh(x) | \e /||| | | \e / /1 \ | \e /| sinh(x) | \e /|| | | | | cos (x)| | |
| / sinh(x)\ | / / sinh(x)\\ / / sinh(x)\\ 2 / / sinh(x)\\ 2*|- + cosh(x)*log(x)|*|x*x *|- + cosh(x)*log(x)|*cos\x /*e + sin\x /|*cos\x / / sinh(x)\ 2 / / sinh(x)\\| | | \e /| | | | \e /|| | x*x *|- + cosh(x)*log(x)|*cos\x /*e + sin\x /|| | | x*x *|- + cosh(x)*log(x)|*cos\x /*e + sin\x /| | | | |1 + -------|*sin(x)| / 2 \|
| \e / | /1 \ | \e /| / 1 2 2*cosh(x)\ | \e /| /1 \ | \e /| sinh(x) \x / \ \x / / \e / /1 \ sinh(x) | \e /|| sinh(x) \ sin\x / / \sin\x // | \x / || |/ 2/ 1 \\ | \x / | | / / 2 \ \ | | x | 2 | | 2 | cos (x)||
|x *|2*|- + cosh(x)*log(x)|*cos\x / + x*|- -- + cosh (x)*log(x) + log(x)*sinh(x) + ---------|*cos\x / + x*|- + cosh(x)*log(x)| *cos\x /*e - ------------------------------------------------------------------------------------------------------------------------- - x*x *|- + cosh(x)*log(x)| *e *sin\x /|*e + ---------------------------------------------------------------------------------------------------------------- 2*|-1 + -------------------------------------------------------------------------------|| ||-1 + tanh |----------------||*|-1 + -------------------------------------------------------------------------------| | | | cos (x)| | | |e x \ sin (x)/ | sin (x)*|1 + -------||
| | \x / | 2 x | \x / / / sinh(x)\\ \x / | x | / / sinh(x)\\ || || | / / sinh(x)\\|| | / / sinh(x)\\ | | | |1 + -------|*sin(x)| | 2 x 2*|-- + e *log(x) - --------------------| x | 2 ||
| | \ x / | \e /| | | | \e /| || || | | \e /||| | | \e /| | | | x | 2 | | | cos (x) x e \x cos(x) / 2*e \ sin (x)/| / 1 \
/ 2/ 1 \\ | \ sin\x / / \ sin\x / /| |\ \sin\x /// \ sin\x / / / 1 \| |e x \ sin (x)/ | x*|1 + ------- + e *log(x) - -- - ------------------------------------------ + ---- - ---------------------|*tanh|----------------|
|-1 + tanh |----------------||*|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + ----------------------------------------------------------------------------------------| 2*|--------------------------------------------------------------------------------------------------------------------- + tanh|----------------||*|-- + e *log(x) - --------------------| | 2 2 / / x\\ x 2 | | / / sinh(x)\\|
| | / / sinh(x)\\|| | / / sinh(x)\\ x | | / / sinh(x)\\ | / / sinh(x)\\|| \x cos(x) / | sin (x) x | \e /| /cos(x)\ cos (x) | | | \e /||
| | | \e /||| | | \e /| | | | \e /| | | \e /||| | log\x / + log|------| | \sin\x //
\ \sin\x /// \ sin\x / / \ sin\x / \sin\x /// \ \sin(x)/ /
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ - -----------------------------------------------------------------------------------------------------------------------------------
/ / sinh(x)\\ / / x\\ / / x\\
| \e /| | \e /| /cos(x)\ | \e /| /cos(x)\
sin\x / log\x / + log|------| log\x / + log|------|
\sin(x)/ \sin(x)/
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
/ / x\\
| \e /| /cos(x)\
log\x / + log|------|
\sin(x)/
$$\frac{- \frac{x \left(- \frac{\left(1 + \frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) \sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} + e^{x} \log{\left(x \right)} + 1 + \frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} - \frac{2 \left(- \frac{\left(1 + \frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) \sin{\left(x \right)}}{\cos{\left(x \right)}} + e^{x} \log{\left(x \right)} + \frac{e^{x}}{x}\right)^{2}}{\log{\left(x^{e^{x}} \right)} + \log{\left(\frac{\cos{\left(x \right)}}{\sin{\left(x \right)}} \right)}} + \frac{2 e^{x}}{x} - \frac{e^{x}}{x^{2}}\right) \tanh{\left(\frac{1}{\sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}} \right)}}{\log{\left(x^{e^{x}} \right)} + \log{\left(\frac{\cos{\left(x \right)}}{\sin{\left(x \right)}} \right)}} + \frac{\left(\frac{x^{e^{\sinh{\left(x \right)}}} \left(- x x^{e^{\sinh{\left(x \right)}}} \left(\log{\left(x \right)} \cosh{\left(x \right)} + \frac{1}{x}\right)^{2} e^{\sinh{\left(x \right)}} \sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)} + x \left(\log{\left(x \right)} \cosh{\left(x \right)} + \frac{1}{x}\right)^{2} e^{\sinh{\left(x \right)}} \cos{\left(x^{e^{\sinh{\left(x \right)}}} \right)} + x \left(\log{\left(x \right)} \sinh{\left(x \right)} + \log{\left(x \right)} \cosh^{2}{\left(x \right)} + \frac{2 \cosh{\left(x \right)}}{x} - \frac{1}{x^{2}}\right) \cos{\left(x^{e^{\sinh{\left(x \right)}}} \right)} - \frac{2 \left(\log{\left(x \right)} \cosh{\left(x \right)} + \frac{1}{x}\right) \left(x x^{e^{\sinh{\left(x \right)}}} \left(\log{\left(x \right)} \cosh{\left(x \right)} + \frac{1}{x}\right) e^{\sinh{\left(x \right)}} \cos{\left(x^{e^{\sinh{\left(x \right)}}} \right)} + \sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}\right) \cos{\left(x^{e^{\sinh{\left(x \right)}}} \right)}}{\sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}} + 2 \left(\log{\left(x \right)} \cosh{\left(x \right)} + \frac{1}{x}\right) \cos{\left(x^{e^{\sinh{\left(x \right)}}} \right)}\right) e^{\sinh{\left(x \right)}} + \frac{2 \left(\frac{x x^{e^{\sinh{\left(x \right)}}} \left(\log{\left(x \right)} \cosh{\left(x \right)} + \frac{1}{x}\right) e^{\sinh{\left(x \right)}} \cos{\left(x^{e^{\sinh{\left(x \right)}}} \right)} + \sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}}{\sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}} - 1\right)^{2} \tanh{\left(\frac{1}{\sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}} \right)}}{x}}{\sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}} + \frac{2 \left(\frac{x x^{e^{\sinh{\left(x \right)}}} \left(\log{\left(x \right)} \cosh{\left(x \right)} + \frac{1}{x}\right) e^{\sinh{\left(x \right)}} \cos{\left(x^{e^{\sinh{\left(x \right)}}} \right)} + \sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}}{\sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}} - 1\right)}{x}\right) \left(\tanh^{2}{\left(\frac{1}{\sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}} \right)} - 1\right)}{\sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}} - \frac{2 \left(\frac{\left(\frac{x x^{e^{\sinh{\left(x \right)}}} \left(\log{\left(x \right)} \cosh{\left(x \right)} + \frac{1}{x}\right) e^{\sinh{\left(x \right)}} \cos{\left(x^{e^{\sinh{\left(x \right)}}} \right)} + \sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}}{\sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}} - 1\right) \left(\tanh^{2}{\left(\frac{1}{\sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}} \right)} - 1\right)}{\sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}} + \tanh{\left(\frac{1}{\sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}} \right)}\right) \left(- \frac{\left(1 + \frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) \sin{\left(x \right)}}{\cos{\left(x \right)}} + e^{x} \log{\left(x \right)} + \frac{e^{x}}{x}\right)}{\log{\left(x^{e^{x}} \right)} + \log{\left(\frac{\cos{\left(x \right)}}{\sin{\left(x \right)}} \right)}}}{\log{\left(x^{e^{x}} \right)} + \log{\left(\frac{\cos{\left(x \right)}}{\sin{\left(x \right)}} \right)}}$$
Tercera derivada
[src]
/ / 2 \ \ / 2 \
| | / / sinh(x)\ / / sinh(x)\\ / / sinh(x)\\\ | | | / / sinh(x)\ / / sinh(x)\\ / / sinh(x)\\\ |
| | | \e / /1 \ | \e /| sinh(x) | \e /|| | | | | \e / /1 \ | \e /| sinh(x) | \e /|| |
| | | x*x *|- + cosh(x)*log(x)|*cos\x /*e + sin\x /| | | / 3 / / 2 \ \ / / 2 \\ \ | | x*x *|- + cosh(x)*log(x)|*cos\x /*e + sin\x /| |
| | | \x / | / 1 \| 3 3 | / / / sinh(x)\ / / sinh(x)\\ / / sinh(x)\\\ \ / 2 \ | / / 2 \ \ | | cos (x)| | | 2 | cos (x)|| | | | \x / | / 1 \ |
| | / / / sinh(x)\ / / sinh(x)\\ / / sinh(x)\\\ / / sinh(x)\\ \ 2*|-1 + -------------------------------------------------------------------------------| *tanh|----------------|| / / sinh(x)\ / / sinh(x)\\ \ / / sinh(x)\ / / sinh(x)\\ / / sinh(x)\\\ / / sinh(x)\ / / sinh(x)\\ / / sinh(x)\\\ / / sinh(x)\ / / sinh(x)\\ / / sinh(x)\\\ / / / sinh(x)\ / / sinh(x)\\ / / sinh(x)\\\ / / sinh(x)\\ \ | | | \e / /1 \ | \e /| sinh(x) | \e /|| | | / / 2 \ \ | | | | cos (x)| | | |1 + -------|*sin(x)| | sin (x)*|1 + -------|| | | / / / sinh(x)\ / / sinh(x)\\ / / sinh(x)\\\ / / sinh(x)\\ \ 2*|-1 + -------------------------------------------------------------------------------| *tanh|----------------| / / sinh(x)\ / / sinh(x)\\ / / sinh(x)\\\|
| | | /1 \ | \e / /1 \ | \e /| sinh(x) | \e /|| | \e /| | | / / sinh(x)\\ | | / / sinh(x)\\|| | \e / /1 \ | \e /| sinh(x)| | \e / /1 \ | \e /| sinh(x) | \e /|| | \e / /1 \ | \e /| sinh(x) | \e /|| | \e / /1 \ | \e /| sinh(x) | \e /|| | /1 \ | \e / /1 \ | \e /| sinh(x) | \e /|| | \e /| | | | | x*x *|- + cosh(x)*log(x)|*cos\x /*e + sin\x /| | | | | cos (x)| | | | | |1 + -------|*sin(x)| | x | 2 | | | 2 x x | 2 || / 4 2 \ / 2 \ / 2 \ | | | /1 \ | \e / /1 \ | \e /| sinh(x) | \e /|| | \e /| | | / / sinh(x)\\ | | / / sinh(x)\\| | \e / /1 \ | \e /| sinh(x) | \e /|||
| | / sinh(x)\ | / / sinh(x)\\ / / sinh(x)\\ 2 / / sinh(x)\\ 2*|- + cosh(x)*log(x)|*|x*x *|- + cosh(x)*log(x)|*cos\x /*e + sin\x /|*cos\x / / sinh(x)\ 2 / / sinh(x)\\| | | \e /| | | | \e /||| | x *|- + cosh(x)*log(x)|*cos\x /*e | / / sinh(x)\ / / sinh(x)\\ / / sinh(x)\\\ | x*x *|- + cosh(x)*log(x)|*cos\x /*e + sin\x /| | x*x *|- + cosh(x)*log(x)|*cos\x /*e + sin\x /| / sinh(x)\ | x*x *|- + cosh(x)*log(x)|*cos\x /*e + sin\x /| | / / sinh(x)\\ / / sinh(x)\\ 2 / / sinh(x)\\ 2*|- + cosh(x)*log(x)|*|x*x *|- + cosh(x)*log(x)|*cos\x /*e + sin\x /|*cos\x / / sinh(x)\ 2 / / sinh(x)\\| | |/ 2/ 1 \\ | \x / | | | | |1 + -------|*sin(x)| / 2 \| | | x | 2 | | |e x \ sin (x)/ | | cos (x) x e 2*e \ sin (x)/| | 3*cos (x) 4*cos (x)| 3 | cos (x)| | cos (x)| | | / sinh(x)\ | / / sinh(x)\\ / / sinh(x)\\ 2 / / sinh(x)\\ 2*|- + cosh(x)*log(x)|*|x*x *|- + cosh(x)*log(x)|*cos\x /*e + sin\x /|*cos\x / / sinh(x)\ 2 / / sinh(x)\\| | | \e /| | | | \e /|| | x*x *|- + cosh(x)*log(x)|*cos\x /*e + sin\x /||
| | \e / | /1 \ | \e /| / 1 2 2*cosh(x)\ | \e /| /1 \ | \e /| sinh(x) \x / \ \x / / \e / /1 \ sinh(x) | \e /|| sinh(x) \ sin\x / / \sin\x //| |1 \x / | | \e / /1 \ | \e /| sinh(x) | \e /|| / sinh(x)\ / / / sinh(x)\\ / / sinh(x)\\ 2 / / sinh(x)\\ / sinh(x)\ 2 / / sinh(x)\\\ | \x / | / 2/ 1 \\ | \x / | 2/ 1 \ sinh(x) / / / sinh(x)\\ / / sinh(x)\\ 2 / / sinh(x)\\ / sinh(x)\ 2 / / sinh(x)\\\ / / sinh(x)\\ / sinh(x)\ / / sinh(x)\ / / sinh(x)\\ / / sinh(x)\\\ / / sinh(x)\\ \e / | \x / | | /1 \ | \e /| / 1 2 2*cosh(x)\ | \e /| /1 \ | \e /| sinh(x) \x / \ \x / / \e / /1 \ sinh(x) | \e /|| sinh(x) / 1 \| ||-1 + tanh |----------------||*|-1 + -------------------------------------------------------------------------------| | | | x | 2 | | 2 | cos (x)|| | |e x \ sin (x)/ | 6*|-- + e *log(x) - --------------------|*|1 + ------- + e *log(x) - -- + ---- - ---------------------| 2*|1 + --------- + ---------|*sin(x) 2*sin (x)*|1 + -------| 2*|1 + -------|*sin(x)| | \e / | /1 \ | \e /| / 1 2 2*cosh(x)\ | \e /| /1 \ | \e /| sinh(x) \x / \ \x / / \e / /1 \ sinh(x) | \e /|| sinh(x) \ sin\x / / \sin\x // | \x / || / / 2 \ \
| / sinh(x)\ / / sinh(x)\\ / / sinh(x)\\ 3*|x *|2*|- + cosh(x)*log(x)|*cos\x / + x*|- -- + cosh (x)*log(x) + log(x)*sinh(x) + ---------|*cos\x / + x*|- + cosh(x)*log(x)| *cos\x /*e - ------------------------------------------------------------------------------------------------------------------------- - x*x *|- + cosh(x)*log(x)| *e *sin\x /|*e + ----------------------------------------------------------------------------------------------------------------| |- + ----------------------------------------------------------|*|x*x *|- + cosh(x)*log(x)|*cos\x /*e + sin\x /| \e / | /1 \ | \e /| / 1 2 2*cosh(x)\ | \e /| /1 \ | \e /| sinh(x) \e / /1 \ sinh(x) | \e /|| sinh(x) 2*|-1 + -------------------------------------------------------------------------------| *|-1 + tanh |----------------|| 4*|-1 + -------------------------------------------------------------------------------| *tanh |----------------| 2*e /1 \ | /1 \ | \e /| / 1 2 2*cosh(x)\ | \e /| /1 \ | \e /| sinh(x) \e / /1 \ sinh(x) | \e /|| | \e /| 2*sinh(x) / sinh(x)\ 2 / / sinh(x)\ / / sinh(x)\\ / / sinh(x)\\\ / / sinh(x)\\ \e / | \e / /1 \ | \e /| sinh(x) | \e /|| / 1 2 2*cosh(x)\ | \e /| sinh(x) sinh(x) 2 / / sinh(x)\\ / / sinh(x)\ / / sinh(x)\\ / / sinh(x)\\\ / sinh(x)\ / / sinh(x)\ / / sinh(x)\\ / / sinh(x)\\\ / / sinh(x)\\ 6*x *|-1 + -------------------------------------------------------------------------------|*|2*|- + cosh(x)*log(x)|*cos\x / + x*|- -- + cosh (x)*log(x) + log(x)*sinh(x) + ---------|*cos\x / + x*|- + cosh(x)*log(x)| *cos\x /*e - ------------------------------------------------------------------------------------------------------------------------- - x*x *|- + cosh(x)*log(x)| *e *sin\x /|*e *tanh|----------------|| || | / / sinh(x)\\|| | / / sinh(x)\\ | | | |e x \ sin (x)/ | sin (x)*|1 + -------|| | x x x 3 6*|-- + e *log(x) - --------------------| \x cos(x) / | 2 2 x 2 | | 4 2 | | 2 | | 2 | | |x *|2*|- + cosh(x)*log(x)|*cos\x / + x*|- -- + cosh (x)*log(x) + log(x)*sinh(x) + ---------|*cos\x / + x*|- + cosh(x)*log(x)| *cos\x /*e - ------------------------------------------------------------------------------------------------------------------------- - x*x *|- + cosh(x)*log(x)| *e *sin\x /|*e + ---------------------------------------------------------------------------------------------------------------- 2*|-1 + -------------------------------------------------------------------------------|| | | cos (x)| |
| \e / /1 \ | \e /| sinh(x) | \e /| | | \x / | 2 x | \x / / / sinh(x)\\ \x / | x | |x / / sinh(x)\\ | \ \x / / x *|2*|- + cosh(x)*log(x)|*cos\x / + x*|- -- + cosh (x)*log(x) + log(x)*sinh(x) + ---------|*cos\x / + x*|- + cosh(x)*log(x)| *cos\x /*e - x*x *|- + cosh(x)*log(x)| *e *sin\x /|*e | / / sinh(x)\\ | | | / / sinh(x)\\|| | / / sinh(x)\\ | | / / sinh(x)\\| 4*x *|- + cosh(x)*log(x)|*|2*|- + cosh(x)*log(x)|*cos\x / + x*|- -- + cosh (x)*log(x) + log(x)*sinh(x) + ---------|*cos\x / + x*|- + cosh(x)*log(x)| *cos\x /*e - x*x *|- + cosh(x)*log(x)| *e *sin\x /|*cos\x /*e \e / /1 \ | \e / /1 \ | \e /| sinh(x) | \e /|| | \e /| 2*sinh(x) 2*x *|x*x *|- + cosh(x)*log(x)|*cos\x /*e + sin\x /|*|- -- + cosh (x)*log(x) + log(x)*sinh(x) + ---------|*cos\x /*e 2*e /1 \ 2| \e /| | \e / /1 \ | \e /| sinh(x) | \e /|| 2*sinh(x) \e / /1 \ | \e / /1 \ | \e /| sinh(x) | \e /|| | \e /| sinh(x) | / / sinh(x)\\ | | \x / | 2 x | \x / / / sinh(x)\\ \x / | | / / sinh(x)\\|| || | | \e /||| | | \e /| | | | 2 x 2*|-- + e *log(x) - --------------------| x | 2 || | x 3*e 2*e 3*e 4*cos (x) 4*cos(x) \x cos(x) / \ sin (x) x cos (x) / \ sin (x) sin (x) / \ sin (x)/ \ sin (x)/ | / 1 \ | | \x / | 2 x | \x / / / sinh(x)\\ \x / | x | / / sinh(x)\\ || | |1 + -------|*sin(x)|
|x*x *|- + cosh(x)*log(x)|*cos\x /*e + sin\x / | | \ x / | \e /| | | / sinh(x)\ / / / sinh(x)\\ / 2 \ / / sinh(x)\\ 2 / / sinh(x)\\ 3 / / sinh(x)\\ / sinh(x)\ 2 / / sinh(x)\\ sinh(x) 3 / / sinh(x)\\ / sinh(x)\ 3 / / sinh(x)\\ / / sinh(x)\\ / sinh(x)\ / / sinh(x)\\\ | | \e /| | | \x / | 2 x | \x / \x / | | | \e /| | | | | \e /||| sinh(x) 2 / / sinh(x)\ / / sinh(x)\\ / / sinh(x)\\\ | | \e /| | | | \e /|| \x / | \x / | 2 x | \x / \x / | 2*x *|- + cosh(x)*log(x)| *|x*x *|- + cosh(x)*log(x)|*cos\x /*e + sin\x /|*cos\x /*e \ \x / / | 2 x | 6*x *|- + cosh(x)*log(x)| *cos \x /*|x*x *|- + cosh(x)*log(x)|*cos\x /*e + sin\x /|*e 3*x *|- + cosh(x)*log(x)|*|x*x *|- + cosh(x)*log(x)|*cos\x /*e + sin\x /|*cos\x /*e | | \e /| | | \ x / | \e /| | | | \e /||| |\ \sin\x /// \ sin\x / / / 1 \| | cos (x) x e \x cos(x) / 2*e \ sin (x)/| x*|e *log(x) - ---- + ---- + ---- + --------- + -------- + ------------------------------------------ - ------------------------------------------------------------------------------------------------------- - ------------------------------------ - ----------------------- + ----------------------|*tanh|----------------| | | \ x / | \e /| | | | \e /| || | x | 2 | |
/ 2/ 1 \\ | \x / \ \ sin\x / / / \e / | / 1 2 2*cosh(x)\ | \e /| |2 3 3*cosh(x) 3*cosh (x) 3*sinh(x) | | \e /| /1 \ | \e /| sinh(x) /1 \ | \e /| 2*sinh(x) \e / /1 \ sinh(x) | \e /| 2*e /1 \ | \e /| 2*sinh(x) \e / /1 \ 2*sinh(x) | \e /| /1 \ / 1 2 2*cosh(x)\ | \e /| sinh(x) \e / /1 \ / 1 2 2*cosh(x)\ sinh(x) | \e /|| sinh(x) \ sin\x / / \ \ x / / \ sin\x / / \ \sin\x /// 2*e /1 \ | \e / /1 \ | \e /| sinh(x) | \e /|| 2*sinh(x) \ sin\x / / \sin\x // \ \ x / / \x / \ \x / / \ x / \x / \ \x / / \x / \ \x / / \ sin\x / / \ sin\x / / \sin\x //| 3*|--------------------------------------------------------------------------------------------------------------------- + tanh|----------------||*|1 + ------- + e *log(x) - -- - ------------------------------------------ + ---- - ---------------------| | 2 3 x 3 sin(x) 2 / / x\\ cos(x) 3 cos(x) | | / / sinh(x)\\| / 2/ 1 \\ | \ sin\x / / \ sin\x / /| |e x \ sin (x)/ |
|-1 + tanh |----------------||*|------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + x *|3*|- -- + cosh (x)*log(x) + log(x)*sinh(x) + ---------|*cos\x / + x*|-- + cosh (x)*log(x) + cosh(x)*log(x) - --------- + ---------- + --------- + 3*cosh(x)*log(x)*sinh(x)|*cos\x / + 3*|- + cosh(x)*log(x)| *cos\x /*e + x*|- + cosh(x)*log(x)| *cos\x /*e - 3*x *|- + cosh(x)*log(x)| *e *sin\x / - x*x *|- + cosh(x)*log(x)| *cos\x /*e - 3*x*x *|- + cosh(x)*log(x)| *e *sin\x / + 3*x*|- + cosh(x)*log(x)|*|- -- + cosh (x)*log(x) + log(x)*sinh(x) + ---------|*cos\x /*e - 3*x*x *|- + cosh(x)*log(x)|*|- -- + cosh (x)*log(x) + log(x)*sinh(x) + ---------|*e *sin\x /|*e - -------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------ + 2*x *|- + cosh(x)*log(x)| *|x*x *|- + cosh(x)*log(x)|*cos\x /*e + sin\x /|*e + ----------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| | / / sinh(x)\\ | / / sinh(x)\\|| | 2 2 / / x\\ x 2 | | x x sin (x) / / / x\\ \ | \e /| /cos(x)\ cos (x) | | | \e /|| 3*|-1 + tanh |----------------||*|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + ----------------------------------------------------------------------------------------|*|-- + e *log(x) - --------------------|
| | / / sinh(x)\\|| | 2 x | | 2 x | | 3 2 x x | \x / \x / \x / \x / \x / \x / | 2 x | \x / | 2 x | | x x / / sinh(x)\\ \x / \ \x / / / / sinh(x)\\ / / sinh(x)\\ / / sinh(x)\\ / / sinh(x)\\ / / sinh(x)\\ / / sinh(x)\\ / / sinh(x)\\ | | | \e /| | | \e /||| | sin (x) x | \e /| /cos(x)\ cos (x) | | | | \e /| /cos(x)\| log\x / + log|------| | \sin\x // | | / / sinh(x)\\|| | / / sinh(x)\\ x | \x cos(x) /
| | | \e /||| | x \ \ x / \x x / \ x / \ x / / 2 | \e /| 2 | \e /| | \e /| | \e /| | \e /| 2| \e /| | \e /| | \e /| | \ sin\x / \sin\x /// | log\x / + log|------| | | |log\x / + log|------|| \sin(x)/ | | | | \e /||| | | \e /| |
\ \sin\x /// \ x *sin\x / x *sin\x / sin\x / sin\x / sin\x / sin \x / x*sin\x / x*sin\x / / \ \sin(x)/ / \ \ \sin(x)// / \ \sin\x /// \ sin\x / /
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
/ / sinh(x)\\ / / x\\ / / x\\ / / / x\\ \ / / sinh(x)\\
2| \e /| | \e /| /cos(x)\ | \e /| /cos(x)\ | | \e /| /cos(x)\| | \e /|
sin \x / log\x / + log|------| log\x / + log|------| |log\x / + log|------||*sin\x /
\sin(x)/ \sin(x)/ \ \sin(x)//
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
/ / x\\
| \e /| /cos(x)\
log\x / + log|------|
\sin(x)/
$$\frac{- \frac{x \left(- \frac{2 \left(1 + \frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) \sin^{3}{\left(x \right)}}{\cos^{3}{\left(x \right)}} + \frac{2 \left(1 + \frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) \sin{\left(x \right)}}{\cos{\left(x \right)}} - \frac{2 \left(1 + \frac{4 \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} + \frac{3 \cos^{4}{\left(x \right)}}{\sin^{4}{\left(x \right)}}\right) \sin{\left(x \right)}}{\cos{\left(x \right)}} + e^{x} \log{\left(x \right)} + \frac{4 \cos{\left(x \right)}}{\sin{\left(x \right)}} + \frac{4 \cos^{3}{\left(x \right)}}{\sin^{3}{\left(x \right)}} - \frac{6 \left(- \frac{\left(1 + \frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) \sin{\left(x \right)}}{\cos{\left(x \right)}} + e^{x} \log{\left(x \right)} + \frac{e^{x}}{x}\right) \left(- \frac{\left(1 + \frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) \sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} + e^{x} \log{\left(x \right)} + 1 + \frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} + \frac{2 e^{x}}{x} - \frac{e^{x}}{x^{2}}\right)}{\log{\left(x^{e^{x}} \right)} + \log{\left(\frac{\cos{\left(x \right)}}{\sin{\left(x \right)}} \right)}} + \frac{6 \left(- \frac{\left(1 + \frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) \sin{\left(x \right)}}{\cos{\left(x \right)}} + e^{x} \log{\left(x \right)} + \frac{e^{x}}{x}\right)^{3}}{\left(\log{\left(x^{e^{x}} \right)} + \log{\left(\frac{\cos{\left(x \right)}}{\sin{\left(x \right)}} \right)}\right)^{2}} + \frac{3 e^{x}}{x} - \frac{3 e^{x}}{x^{2}} + \frac{2 e^{x}}{x^{3}}\right) \tanh{\left(\frac{1}{\sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}} \right)}}{\log{\left(x^{e^{x}} \right)} + \log{\left(\frac{\cos{\left(x \right)}}{\sin{\left(x \right)}} \right)}} - \frac{3 \left(\frac{x^{e^{\sinh{\left(x \right)}}} \left(- x x^{e^{\sinh{\left(x \right)}}} \left(\log{\left(x \right)} \cosh{\left(x \right)} + \frac{1}{x}\right)^{2} e^{\sinh{\left(x \right)}} \sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)} + x \left(\log{\left(x \right)} \cosh{\left(x \right)} + \frac{1}{x}\right)^{2} e^{\sinh{\left(x \right)}} \cos{\left(x^{e^{\sinh{\left(x \right)}}} \right)} + x \left(\log{\left(x \right)} \sinh{\left(x \right)} + \log{\left(x \right)} \cosh^{2}{\left(x \right)} + \frac{2 \cosh{\left(x \right)}}{x} - \frac{1}{x^{2}}\right) \cos{\left(x^{e^{\sinh{\left(x \right)}}} \right)} - \frac{2 \left(\log{\left(x \right)} \cosh{\left(x \right)} + \frac{1}{x}\right) \left(x x^{e^{\sinh{\left(x \right)}}} \left(\log{\left(x \right)} \cosh{\left(x \right)} + \frac{1}{x}\right) e^{\sinh{\left(x \right)}} \cos{\left(x^{e^{\sinh{\left(x \right)}}} \right)} + \sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}\right) \cos{\left(x^{e^{\sinh{\left(x \right)}}} \right)}}{\sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}} + 2 \left(\log{\left(x \right)} \cosh{\left(x \right)} + \frac{1}{x}\right) \cos{\left(x^{e^{\sinh{\left(x \right)}}} \right)}\right) e^{\sinh{\left(x \right)}} + \frac{2 \left(\frac{x x^{e^{\sinh{\left(x \right)}}} \left(\log{\left(x \right)} \cosh{\left(x \right)} + \frac{1}{x}\right) e^{\sinh{\left(x \right)}} \cos{\left(x^{e^{\sinh{\left(x \right)}}} \right)} + \sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}}{\sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}} - 1\right)^{2} \tanh{\left(\frac{1}{\sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}} \right)}}{x}}{\sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}} + \frac{2 \left(\frac{x x^{e^{\sinh{\left(x \right)}}} \left(\log{\left(x \right)} \cosh{\left(x \right)} + \frac{1}{x}\right) e^{\sinh{\left(x \right)}} \cos{\left(x^{e^{\sinh{\left(x \right)}}} \right)} + \sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}}{\sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}} - 1\right)}{x}\right) \left(\tanh^{2}{\left(\frac{1}{\sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}} \right)} - 1\right) \left(- \frac{\left(1 + \frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) \sin{\left(x \right)}}{\cos{\left(x \right)}} + e^{x} \log{\left(x \right)} + \frac{e^{x}}{x}\right)}{\left(\log{\left(x^{e^{x}} \right)} + \log{\left(\frac{\cos{\left(x \right)}}{\sin{\left(x \right)}} \right)}\right) \sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}} - \frac{3 \left(\frac{\left(\frac{x x^{e^{\sinh{\left(x \right)}}} \left(\log{\left(x \right)} \cosh{\left(x \right)} + \frac{1}{x}\right) e^{\sinh{\left(x \right)}} \cos{\left(x^{e^{\sinh{\left(x \right)}}} \right)} + \sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}}{\sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}} - 1\right) \left(\tanh^{2}{\left(\frac{1}{\sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}} \right)} - 1\right)}{\sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}} + \tanh{\left(\frac{1}{\sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}} \right)}\right) \left(- \frac{\left(1 + \frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) \sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} + e^{x} \log{\left(x \right)} + 1 + \frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} - \frac{2 \left(- \frac{\left(1 + \frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) \sin{\left(x \right)}}{\cos{\left(x \right)}} + e^{x} \log{\left(x \right)} + \frac{e^{x}}{x}\right)^{2}}{\log{\left(x^{e^{x}} \right)} + \log{\left(\frac{\cos{\left(x \right)}}{\sin{\left(x \right)}} \right)}} + \frac{2 e^{x}}{x} - \frac{e^{x}}{x^{2}}\right)}{\log{\left(x^{e^{x}} \right)} + \log{\left(\frac{\cos{\left(x \right)}}{\sin{\left(x \right)}} \right)}} + \frac{\left(\tanh^{2}{\left(\frac{1}{\sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}} \right)} - 1\right) \left(2 x^{2 e^{\sinh{\left(x \right)}}} \left(\log{\left(x \right)} \cosh{\left(x \right)} + \frac{1}{x}\right)^{2} \left(x x^{e^{\sinh{\left(x \right)}}} \left(\log{\left(x \right)} \cosh{\left(x \right)} + \frac{1}{x}\right) e^{\sinh{\left(x \right)}} \cos{\left(x^{e^{\sinh{\left(x \right)}}} \right)} + \sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}\right) e^{2 \sinh{\left(x \right)}} + \frac{6 x^{2 e^{\sinh{\left(x \right)}}} \left(\log{\left(x \right)} \cosh{\left(x \right)} + \frac{1}{x}\right)^{2} \left(x x^{e^{\sinh{\left(x \right)}}} \left(\log{\left(x \right)} \cosh{\left(x \right)} + \frac{1}{x}\right) e^{\sinh{\left(x \right)}} \cos{\left(x^{e^{\sinh{\left(x \right)}}} \right)} + \sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}\right) e^{2 \sinh{\left(x \right)}} \cos^{2}{\left(x^{e^{\sinh{\left(x \right)}}} \right)}}{\sin^{2}{\left(x^{e^{\sinh{\left(x \right)}}} \right)}} - \frac{4 x^{2 e^{\sinh{\left(x \right)}}} \left(\log{\left(x \right)} \cosh{\left(x \right)} + \frac{1}{x}\right) \left(- x x^{e^{\sinh{\left(x \right)}}} \left(\log{\left(x \right)} \cosh{\left(x \right)} + \frac{1}{x}\right)^{2} e^{\sinh{\left(x \right)}} \sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)} + x \left(\log{\left(x \right)} \cosh{\left(x \right)} + \frac{1}{x}\right)^{2} e^{\sinh{\left(x \right)}} \cos{\left(x^{e^{\sinh{\left(x \right)}}} \right)} + x \left(\log{\left(x \right)} \sinh{\left(x \right)} + \log{\left(x \right)} \cosh^{2}{\left(x \right)} + \frac{2 \cosh{\left(x \right)}}{x} - \frac{1}{x^{2}}\right) \cos{\left(x^{e^{\sinh{\left(x \right)}}} \right)} + 2 \left(\log{\left(x \right)} \cosh{\left(x \right)} + \frac{1}{x}\right) \cos{\left(x^{e^{\sinh{\left(x \right)}}} \right)}\right) e^{2 \sinh{\left(x \right)}} \cos{\left(x^{e^{\sinh{\left(x \right)}}} \right)}}{\sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}} - \frac{2 x^{e^{\sinh{\left(x \right)}}} \left(\log{\left(x \right)} \cosh{\left(x \right)} + \frac{1}{x}\right)^{2} \left(x x^{e^{\sinh{\left(x \right)}}} \left(\log{\left(x \right)} \cosh{\left(x \right)} + \frac{1}{x}\right) e^{\sinh{\left(x \right)}} \cos{\left(x^{e^{\sinh{\left(x \right)}}} \right)} + \sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}\right) e^{2 \sinh{\left(x \right)}} \cos{\left(x^{e^{\sinh{\left(x \right)}}} \right)}}{\sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}} - \frac{2 x^{e^{\sinh{\left(x \right)}}} \left(x x^{e^{\sinh{\left(x \right)}}} \left(\log{\left(x \right)} \cosh{\left(x \right)} + \frac{1}{x}\right) e^{\sinh{\left(x \right)}} \cos{\left(x^{e^{\sinh{\left(x \right)}}} \right)} + \sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}\right) \left(\log{\left(x \right)} \sinh{\left(x \right)} + \log{\left(x \right)} \cosh^{2}{\left(x \right)} + \frac{2 \cosh{\left(x \right)}}{x} - \frac{1}{x^{2}}\right) e^{\sinh{\left(x \right)}} \cos{\left(x^{e^{\sinh{\left(x \right)}}} \right)}}{\sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}} + x^{e^{\sinh{\left(x \right)}}} \left(- x x^{2 e^{\sinh{\left(x \right)}}} \left(\log{\left(x \right)} \cosh{\left(x \right)} + \frac{1}{x}\right)^{3} e^{2 \sinh{\left(x \right)}} \cos{\left(x^{e^{\sinh{\left(x \right)}}} \right)} - 3 x x^{e^{\sinh{\left(x \right)}}} \left(\log{\left(x \right)} \cosh{\left(x \right)} + \frac{1}{x}\right)^{3} e^{2 \sinh{\left(x \right)}} \sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)} - 3 x x^{e^{\sinh{\left(x \right)}}} \left(\log{\left(x \right)} \cosh{\left(x \right)} + \frac{1}{x}\right) \left(\log{\left(x \right)} \sinh{\left(x \right)} + \log{\left(x \right)} \cosh^{2}{\left(x \right)} + \frac{2 \cosh{\left(x \right)}}{x} - \frac{1}{x^{2}}\right) e^{\sinh{\left(x \right)}} \sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)} + x \left(\log{\left(x \right)} \cosh{\left(x \right)} + \frac{1}{x}\right)^{3} e^{2 \sinh{\left(x \right)}} \cos{\left(x^{e^{\sinh{\left(x \right)}}} \right)} + 3 x \left(\log{\left(x \right)} \cosh{\left(x \right)} + \frac{1}{x}\right) \left(\log{\left(x \right)} \sinh{\left(x \right)} + \log{\left(x \right)} \cosh^{2}{\left(x \right)} + \frac{2 \cosh{\left(x \right)}}{x} - \frac{1}{x^{2}}\right) e^{\sinh{\left(x \right)}} \cos{\left(x^{e^{\sinh{\left(x \right)}}} \right)} + x \left(3 \log{\left(x \right)} \sinh{\left(x \right)} \cosh{\left(x \right)} + \log{\left(x \right)} \cosh^{3}{\left(x \right)} + \log{\left(x \right)} \cosh{\left(x \right)} + \frac{3 \sinh{\left(x \right)}}{x} + \frac{3 \cosh^{2}{\left(x \right)}}{x} - \frac{3 \cosh{\left(x \right)}}{x^{2}} + \frac{2}{x^{3}}\right) \cos{\left(x^{e^{\sinh{\left(x \right)}}} \right)} - 3 x^{e^{\sinh{\left(x \right)}}} \left(\log{\left(x \right)} \cosh{\left(x \right)} + \frac{1}{x}\right)^{2} e^{\sinh{\left(x \right)}} \sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)} + 3 \left(\log{\left(x \right)} \cosh{\left(x \right)} + \frac{1}{x}\right)^{2} e^{\sinh{\left(x \right)}} \cos{\left(x^{e^{\sinh{\left(x \right)}}} \right)} + 3 \left(\log{\left(x \right)} \sinh{\left(x \right)} + \log{\left(x \right)} \cosh^{2}{\left(x \right)} + \frac{2 \cosh{\left(x \right)}}{x} - \frac{1}{x^{2}}\right) \cos{\left(x^{e^{\sinh{\left(x \right)}}} \right)}\right) e^{\sinh{\left(x \right)}} + \frac{6 x^{e^{\sinh{\left(x \right)}}} \left(\frac{x x^{e^{\sinh{\left(x \right)}}} \left(\log{\left(x \right)} \cosh{\left(x \right)} + \frac{1}{x}\right) e^{\sinh{\left(x \right)}} \cos{\left(x^{e^{\sinh{\left(x \right)}}} \right)} + \sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}}{\sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}} - 1\right) \left(- x x^{e^{\sinh{\left(x \right)}}} \left(\log{\left(x \right)} \cosh{\left(x \right)} + \frac{1}{x}\right)^{2} e^{\sinh{\left(x \right)}} \sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)} + x \left(\log{\left(x \right)} \cosh{\left(x \right)} + \frac{1}{x}\right)^{2} e^{\sinh{\left(x \right)}} \cos{\left(x^{e^{\sinh{\left(x \right)}}} \right)} + x \left(\log{\left(x \right)} \sinh{\left(x \right)} + \log{\left(x \right)} \cosh^{2}{\left(x \right)} + \frac{2 \cosh{\left(x \right)}}{x} - \frac{1}{x^{2}}\right) \cos{\left(x^{e^{\sinh{\left(x \right)}}} \right)} - \frac{2 \left(\log{\left(x \right)} \cosh{\left(x \right)} + \frac{1}{x}\right) \left(x x^{e^{\sinh{\left(x \right)}}} \left(\log{\left(x \right)} \cosh{\left(x \right)} + \frac{1}{x}\right) e^{\sinh{\left(x \right)}} \cos{\left(x^{e^{\sinh{\left(x \right)}}} \right)} + \sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}\right) \cos{\left(x^{e^{\sinh{\left(x \right)}}} \right)}}{\sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}} + 2 \left(\log{\left(x \right)} \cosh{\left(x \right)} + \frac{1}{x}\right) \cos{\left(x^{e^{\sinh{\left(x \right)}}} \right)}\right) e^{\sinh{\left(x \right)}} \tanh{\left(\frac{1}{\sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}} \right)}}{x \sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}} + \frac{3 x^{e^{\sinh{\left(x \right)}}} \left(\log{\left(x \right)} \cosh{\left(x \right)} + \frac{1}{x}\right) \left(x x^{e^{\sinh{\left(x \right)}}} \left(\log{\left(x \right)} \cosh{\left(x \right)} + \frac{1}{x}\right) e^{\sinh{\left(x \right)}} \cos{\left(x^{e^{\sinh{\left(x \right)}}} \right)} + \sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}\right) e^{\sinh{\left(x \right)}} \cos{\left(x^{e^{\sinh{\left(x \right)}}} \right)}}{x \sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}} - \frac{x^{e^{\sinh{\left(x \right)}}} \left(- x x^{e^{\sinh{\left(x \right)}}} \left(\log{\left(x \right)} \cosh{\left(x \right)} + \frac{1}{x}\right)^{2} e^{\sinh{\left(x \right)}} \sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)} + x \left(\log{\left(x \right)} \cosh{\left(x \right)} + \frac{1}{x}\right)^{2} e^{\sinh{\left(x \right)}} \cos{\left(x^{e^{\sinh{\left(x \right)}}} \right)} + x \left(\log{\left(x \right)} \sinh{\left(x \right)} + \log{\left(x \right)} \cosh^{2}{\left(x \right)} + \frac{2 \cosh{\left(x \right)}}{x} - \frac{1}{x^{2}}\right) \cos{\left(x^{e^{\sinh{\left(x \right)}}} \right)} + 2 \left(\log{\left(x \right)} \cosh{\left(x \right)} + \frac{1}{x}\right) \cos{\left(x^{e^{\sinh{\left(x \right)}}} \right)}\right) e^{\sinh{\left(x \right)}}}{x} + \frac{3 \left(x^{e^{\sinh{\left(x \right)}}} \left(- x x^{e^{\sinh{\left(x \right)}}} \left(\log{\left(x \right)} \cosh{\left(x \right)} + \frac{1}{x}\right)^{2} e^{\sinh{\left(x \right)}} \sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)} + x \left(\log{\left(x \right)} \cosh{\left(x \right)} + \frac{1}{x}\right)^{2} e^{\sinh{\left(x \right)}} \cos{\left(x^{e^{\sinh{\left(x \right)}}} \right)} + x \left(\log{\left(x \right)} \sinh{\left(x \right)} + \log{\left(x \right)} \cosh^{2}{\left(x \right)} + \frac{2 \cosh{\left(x \right)}}{x} - \frac{1}{x^{2}}\right) \cos{\left(x^{e^{\sinh{\left(x \right)}}} \right)} - \frac{2 \left(\log{\left(x \right)} \cosh{\left(x \right)} + \frac{1}{x}\right) \left(x x^{e^{\sinh{\left(x \right)}}} \left(\log{\left(x \right)} \cosh{\left(x \right)} + \frac{1}{x}\right) e^{\sinh{\left(x \right)}} \cos{\left(x^{e^{\sinh{\left(x \right)}}} \right)} + \sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}\right) \cos{\left(x^{e^{\sinh{\left(x \right)}}} \right)}}{\sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}} + 2 \left(\log{\left(x \right)} \cosh{\left(x \right)} + \frac{1}{x}\right) \cos{\left(x^{e^{\sinh{\left(x \right)}}} \right)}\right) e^{\sinh{\left(x \right)}} + \frac{2 \left(\frac{x x^{e^{\sinh{\left(x \right)}}} \left(\log{\left(x \right)} \cosh{\left(x \right)} + \frac{1}{x}\right) e^{\sinh{\left(x \right)}} \cos{\left(x^{e^{\sinh{\left(x \right)}}} \right)} + \sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}}{\sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}} - 1\right)^{2} \tanh{\left(\frac{1}{\sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}} \right)}}{x}\right)}{x} - \frac{\left(x x^{e^{\sinh{\left(x \right)}}} \left(\log{\left(x \right)} \cosh{\left(x \right)} + \frac{1}{x}\right) e^{\sinh{\left(x \right)}} \cos{\left(x^{e^{\sinh{\left(x \right)}}} \right)} + \sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}\right) \left(\frac{x^{e^{\sinh{\left(x \right)}}} \left(\log{\left(x \right)} \cosh{\left(x \right)} + \frac{1}{x}\right) e^{\sinh{\left(x \right)}} \cos{\left(x^{e^{\sinh{\left(x \right)}}} \right)}}{\sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}} + \frac{1}{x}\right)}{x} + \frac{2 \left(\frac{x x^{e^{\sinh{\left(x \right)}}} \left(\log{\left(x \right)} \cosh{\left(x \right)} + \frac{1}{x}\right) e^{\sinh{\left(x \right)}} \cos{\left(x^{e^{\sinh{\left(x \right)}}} \right)} + \sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}}{\sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}} - 1\right)^{3} \left(\tanh^{2}{\left(\frac{1}{\sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}} \right)} - 1\right)}{x^{2} \sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}} + \frac{4 \left(\frac{x x^{e^{\sinh{\left(x \right)}}} \left(\log{\left(x \right)} \cosh{\left(x \right)} + \frac{1}{x}\right) e^{\sinh{\left(x \right)}} \cos{\left(x^{e^{\sinh{\left(x \right)}}} \right)} + \sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}}{\sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}} - 1\right)^{3} \tanh^{2}{\left(\frac{1}{\sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}} \right)}}{x^{2} \sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}} + \frac{x x^{e^{\sinh{\left(x \right)}}} \left(\log{\left(x \right)} \cosh{\left(x \right)} + \frac{1}{x}\right) e^{\sinh{\left(x \right)}} \cos{\left(x^{e^{\sinh{\left(x \right)}}} \right)} + \sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}}{x^{2}}\right)}{\sin^{2}{\left(x^{e^{\sinh{\left(x \right)}}} \right)}}}{\log{\left(x^{e^{x}} \right)} + \log{\left(\frac{\cos{\left(x \right)}}{\sin{\left(x \right)}} \right)}}$$