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
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¿Cómo usar?
- Derivada de:
-
Derivada de e^-1
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Derivada de (x^2)'
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Derivada de y
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Derivada de (x^5+1)
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Expresiones idénticas
- x*tanh^ dos (x/(x*sin(x^(exp(sinh(x))))))+(log(x^exp(x))+log(cos(x)/sin(x)))
- x multiplicar por tangente de gente hiperbólica de al cuadrado (x dividir por (x multiplicar por seno de (x en el grado ( exponente de ( seno hiperbólico de (x)))))) más ( logaritmo de (x en el grado exponente de (x)) más logaritmo de ( coseno de (x) dividir por seno de (x)))
- x multiplicar por tangente de gente hiperbólica de en el grado dos (x dividir por (x multiplicar por seno de (x en el grado ( exponente de ( seno hiperbólico de (x)))))) más ( logaritmo de (x en el grado exponente de (x)) más logaritmo de ( coseno de (x) dividir por seno de (x)))
- x*tanh2(x/(x*sin(x(exp(sinh(x))))))+(log(xexp(x))+log(cos(x)/sin(x)))
- x*tanh2x/x*sinxexpsinhx+logxexpx+logcosx/sinx
- x*tanh²(x/(x*sin(x^(exp(sinh(x))))))+(log(x^exp(x))+log(cos(x)/sin(x)))
- x*tanh en el grado 2(x/(x*sin(x en el grado (exp(sinh(x))))))+(log(x en el grado exp(x))+log(cos(x)/sin(x)))
- xtanh^2(x/(xsin(x^(exp(sinh(x))))))+(log(x^exp(x))+log(cos(x)/sin(x)))
- xtanh2(x/(xsin(x(exp(sinh(x))))))+(log(xexp(x))+log(cos(x)/sin(x)))
- xtanh2x/xsinxexpsinhx+logxexpx+logcosx/sinx
- xtanh^2x/xsinx^expsinhx+logx^expx+logcosx/sinx
- x*tanh^2(x dividir por (x*sin(x^(exp(sinh(x))))))+(log(x^exp(x))+log(cos(x) dividir por sin(x)))
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Expresiones semejantes
- x*tanh^2(x/(x*sin(x^(exp(sinh(x))))))+(log(x^exp(x))-log(cos(x)/sin(x)))
- x*tanh^2(x/(x*sin(x^(exp(sinh(x))))))-(log(x^exp(x))+log(cos(x)/sin(x)))
- x*tanh^2(x/(x*sin(x^(exp(sinh(x))))))+(log(x^exp(x))+log(cosx/sinx))
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Expresiones con funciones
- Seno sin
- sin(sin(x))
- sin^2*2x
- sin(x/5)
- sin(3*x)^(2)
- sin(8*x)
- Exponente exp
- exp(x^1/2)
- exp(2*x)
- exp(y)
- Logaritmo log
- log(x^-1)
- log(log(x))
- log(x^4+x)
- log(e)^x
- log(e^x)
- Exponente exp
- exp(x^1/2)
- exp(2*x)
- exp(y)
- Logaritmo log
- log(x^-1)
- log(log(x))
- log(x^4+x)
- log(e)^x
- log(e^x)
- Coseno cos
- cos(x)/2
- cosx/lnx
- cos(x)^(1/2)
- cos(x)*log(x)
- cos(x)^(23)
- Seno sin
- sin(sin(x))
- sin^2*2x
- sin(x/5)
- sin(3*x)^(2)
- sin(8*x)
Derivada de x*tanh^2(x/(x*sin(x^(exp(sinh(x))))))+(log(x^exp(x))+log(cos(x)/sin(x)))
Solución
Ha introducido
[src]
/ / x\\
2/ x \ | \e /| /cos(x)\
x*tanh |------------------| + log\x / + log|------|
| / / sinh(x)\\| \sin(x)/
| | \e /||
\x*sin\x //
$$x \tanh^{2}{\left(\frac{x}{x \sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}} \right)} + \left(\log{\left(x^{e^{x}} \right)} + \log{\left(\frac{\cos{\left(x \right)}}{\sin{\left(x \right)}} \right)}\right)$$
x*tanh(x/((x*sin(x^exp(sinh(x))))))^2 + log(x^exp(x)) + log(cos(x)/sin(x))
Primera derivada
[src]
/ 2 \
| cos (x)| / / / sinh(x)\\ / sinh(x)\ / sinh(x) \ / / sinh(x)\\\
|-1 - -------|*sin(x) | | \e /| \e / |e sinh(x) | | \e /||
x | 2 | | - sin\x / - x*x *|-------- + cosh(x)*e *log(x)|*cos\x /|
2/ x \ e x \ sin (x)/ / 2/ x \\ | 1 \ x / | / x \
tanh |------------------| + -- + e *log(x) + --------------------- + 2*x*|1 - tanh |------------------||*|------------------ + ----------------------------------------------------------------------------------------|*tanh|------------------|
| / / sinh(x)\\| x cos(x) | | / / sinh(x)\\|| | / / sinh(x)\\ / / sinh(x)\\ | | / / sinh(x)\\|
| | \e /|| | | | \e /||| | | \e /| 2| \e /| | | | \e /||
\x*sin\x // \ \x*sin\x /// \x*sin\x / x*sin \x / / \x*sin\x //
$$2 x \left(1 - \tanh^{2}{\left(\frac{x}{x \sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}} \right)}\right) \left(\frac{1}{x \sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}} + \frac{- x x^{e^{\sinh{\left(x \right)}}} \left(e^{\sinh{\left(x \right)}} \log{\left(x \right)} \cosh{\left(x \right)} + \frac{e^{\sinh{\left(x \right)}}}{x}\right) \cos{\left(x^{e^{\sinh{\left(x \right)}}} \right)} - \sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}}{x \sin^{2}{\left(x^{e^{\sinh{\left(x \right)}}} \right)}}\right) \tanh{\left(\frac{x}{x \sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}} \right)} + \frac{\left(-1 - \frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) \sin{\left(x \right)}}{\cos{\left(x \right)}} + e^{x} \log{\left(x \right)} + \tanh^{2}{\left(\frac{x}{x \sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}} \right)} + \frac{e^{x}}{x}$$
Segunda derivada
[src]
2 2
/ / 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 /|| | \e / /1 \ | \e /| sinh(x) | \e /|| | \e / /1 \ | \e /| sinh(x) | \e /|| | /1 \ | \e / /1 \ | \e /| sinh(x) | \e /|| | \e /| |
2 | x*x *|- + cosh(x)*log(x)|*cos\x /*e + sin\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)\ | / / 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 \ / 2/ 1 \\ | \x / | | \x / | 2/ 1 \ / 2/ 1 \\ / 2/ 1 \\ | \x / | / 1 \ \e / / 2/ 1 \\ | /1 \ | \e /| / 1 2 2*cosh(x)\ | \e /| /1 \ | \e /| sinh(x) \x / \ \x / / \e / /1 \ sinh(x) | \e /|| sinh(x) / 1 \
2 | cos (x)| 2*|-1 + tanh |----------------|| *|-1 + -------------------------------------------------------------------------------| 4*|-1 + -------------------------------------------------------------------------------| *tanh |----------------|*|-1 + tanh |----------------|| 4*|-1 + tanh |----------------||*|-1 + -------------------------------------------------------------------------------|*tanh|----------------| 2*x *|-1 + tanh |----------------||*|- 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|----------------|
sin (x)*|1 + -------| | | / / sinh(x)\\|| | / / sinh(x)\\ | | / / sinh(x)\\ | | / / sinh(x)\\| | | / / sinh(x)\\|| | | / / sinh(x)\\|| | / / sinh(x)\\ | | / / sinh(x)\\| | | / / sinh(x)\\|| | \x / | 2 x | \x / / / sinh(x)\\ \x / | | / / sinh(x)\\|
2 x x | 2 | | | | \e /||| | | \e /| | | | \e /| | | | \e /|| | | | \e /||| | | | \e /||| | | \e /| | | | \e /|| | | | \e /||| | \ x / | \e /| | | | \e /||
cos (x) x e 2*e \ sin (x)/ \ \sin\x /// \ sin\x / / \ sin\x / / \sin\x // \ \sin\x /// \ \sin\x /// \ sin\x / / \sin\x // \ \sin\x /// \ sin\x / / \sin\x //
1 + ------- + e *log(x) - -- + ---- - --------------------- + ------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------ + ---------------------------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
2 2 x 2 / / sinh(x)\\ / / sinh(x)\\ / / sinh(x)\\ / / sinh(x)\\
sin (x) x cos (x) 2| \e /| 2| \e /| | \e /| 2| \e /|
x*sin \x / x*sin \x / x*sin\x / sin \x /
$$- \frac{2 x^{e^{\sinh{\left(x \right)}}} \left(\tanh^{2}{\left(\frac{1}{\sin{\left(x^{e^{\sinh{\left(x \right)}}} \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)}}{\sin^{2}{\left(x^{e^{\sinh{\left(x \right)}}} \right)}} - \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{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} \left(\tanh^{2}{\left(\frac{1}{\sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}} \right)} - 1\right)^{2}}{x \sin^{2}{\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)^{2} \left(\tanh^{2}{\left(\frac{1}{\sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}} \right)} - 1\right) \tanh^{2}{\left(\frac{1}{\sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}} \right)}}{x \sin^{2}{\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) \left(\tanh^{2}{\left(\frac{1}{\sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}} \right)} - 1\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{2 e^{x}}{x} - \frac{e^{x}}{x^{2}}$$
Tercera derivada
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/ / / sinh(x)\ / / sinh(x)\\ \ \
| | \e / /1 \ | \e /| sinh(x)| |
| | x *|- + cosh(x)*log(x)|*cos\x /*e | / / sinh(x)\ / / sinh(x)\\ / / sinh(x)\\\ |
| |1 \x / | | \e / /1 \ | \e /| sinh(x) | \e /|| / 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) / / / sinh(x)\\ / / sinh(x)\\ 2 / / sinh(x)\\ / sinh(x)\ 2 / / sinh(x)\\\ / / sinh(x)\\ | 2 3 2 3
| / sinh(x)\ / / sinh(x)\\ / / sinh(x)\\ |- + ----------------------------------------------------------|*|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) sinh(x) 2 / / sinh(x)\\ / / sinh(x)\ / / sinh(x)\\ / / 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) 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)\ / / 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)\\ / / 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)\\\ / / / sinh(x)\ / / sinh(x)\\ / / sinh(x)\\\ / / sinh(x)\\ \
| \e / /1 \ | \e /| sinh(x) | \e /| |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 2*e /1 \ 2| \e /| | \e / /1 \ | \e /| sinh(x) | \e /|| 2*sinh(x) \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 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 /| sinh(x)| | \e / /1 \ | \e /| sinh(x) | \e /|| | \e / /1 \ | \e /| sinh(x) | \e /|| | \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 /| | | /1 \ | \e / /1 \ | \e /| sinh(x) | \e /|| | \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 / | | \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)\\ / sinh(x)\ 3 / / sinh(x)\\ / sinh(x)\ / / sinh(x)\\\ | \x / | 2 x | \x / \x / | sinh(x) 2 / / sinh(x)\ / / sinh(x)\\ / / sinh(x)\\\ 6*x *|- + cosh(x)*log(x)| *cos \x /*|x*x *|- + cosh(x)*log(x)|*cos\x /*e + sin\x /|*e 2*x *|- + cosh(x)*log(x)| *|x*x *|- + cosh(x)*log(x)|*cos\x /*e + sin\x /|*cos\x /*e \ \x / / | 2 x | \x / | \x / | 2 x | \x / \x / | 3*x *|- + cosh(x)*log(x)|*|x*x *|- + cosh(x)*log(x)|*cos\x /*e + sin\x /|*cos\x /*e | 2 | x*x *|- + cosh(x)*log(x)|*cos\x /*e + sin\x /| | x*x *|- + cosh(x)*log(x)|*cos\x /*e + sin\x /| | x*x *|- + cosh(x)*log(x)|*cos\x /*e + sin\x /| 2 | x*x *|- + cosh(x)*log(x)|*cos\x /*e + sin\x /| / sinh(x)\ 2 | 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)\\| / 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)\\| / 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)\\|
/ 4 2 \ / 2 \ / 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) /1 \ / 1 2 2*cosh(x)\ | \e /| sinh(x) \e / /1 \ 2*sinh(x) | \e /| \e / /1 \ / 1 2 2*cosh(x)\ sinh(x) | \e /|| sinh(x) \ \ x / / 2*e /1 \ | \e / /1 \ | \e /| sinh(x) | \e /|| 2*sinh(x) \x / \ \x / / \x / \ \x / / \ x / \ \ x / / \x / \ \x / / | / 1 \ / 2/ 1 \\ | \x / | | \x / | 3/ 1 \ / 2/ 1 \\ | \x / | 2/ 1 \ / 2/ 1 \\ / 2/ 1 \\ | \x / | / 1 \ \e / / 2/ 1 \\ | \x / | | /1 \ | \e /| / 1 2 2*cosh(x)\ | \e /| /1 \ | \e /| sinh(x) \x / \ \x / / \e / /1 \ sinh(x) | \e /|| sinh(x) \e / / 2/ 1 \\ | /1 \ | \e /| / 1 2 2*cosh(x)\ | \e /| /1 \ | \e /| sinh(x) \x / \ \x / / \e / /1 \ sinh(x) | \e /|| sinh(x) / 1 \ \e / 2/ 1 \ / 2/ 1 \\ | \x / | | /1 \ | \e /| / 1 2 2*cosh(x)\ | \e /| /1 \ | \e /| sinh(x) \x / \ \x / / \e / /1 \ sinh(x) | \e /|| sinh(x)
| 3*cos (x) 4*cos (x)| 3 | cos (x)| | cos (x)| 2*|-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*|- + cosh(x)*log(x)|*|- -- + cosh (x)*log(x) + log(x)*sinh(x) + ---------|*cos\x /*e + 3*x*x *|- + cosh(x)*log(x)| *e *sin\x / + 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 - -------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------|*tanh|----------------| 6*|-1 + tanh |----------------|| *|-1 + -------------------------------------------------------------------------------| 8*|-1 + -------------------------------------------------------------------------------| *tanh |----------------|*|-1 + tanh |----------------|| 12*|-1 + -------------------------------------------------------------------------------| *tanh |----------------|*|-1 + tanh |----------------|| 16*|-1 + tanh |----------------|| *|-1 + -------------------------------------------------------------------------------| *tanh|----------------| 6*x *|-1 + tanh |----------------|| *|-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 6*x *|-1 + tanh |----------------||*|- 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|----------------| 12*x *tanh |----------------|*|-1 + tanh |----------------||*|-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
2*|1 + --------- + ---------|*sin(x) 2*sin (x)*|1 + -------| 2*|1 + -------|*sin(x) | | / / sinh(x)\\|| | 2 x | | 2 x | | 3 2 x x | \x / \x / \x / \x / \x / | 2 x | \x / \x / | 2 x | | x \x / \ \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)\\|| | | / / sinh(x)\\|| | / / sinh(x)\\ | | / / sinh(x)\\| | | / / sinh(x)\\|| | / / sinh(x)\\ | | \x / | 2 x | \x / / / sinh(x)\\ \x / | | | / / sinh(x)\\|| | \x / | 2 x | \x / / / sinh(x)\\ \x / | | / / sinh(x)\\| | / / sinh(x)\\| | | / / sinh(x)\\|| | / / sinh(x)\\ | | \x / | 2 x | \x / / / sinh(x)\\ \x / |
x x x 3 | 4 2 | | 2 | | 2 | | | | \e /||| | x \ \ x / \x x / \ x / \ x / / 2| \e /| | \e /| | \e /| | \e /| | \e /| | | | \e /|| | | | \e /||| | | \e /| | | | \e /| | | | \e /|| | | | \e /||| | | \e /| | | | \e /|| | | | \e /||| | | | \e /||| | | \e /| | | | \e /|| | | | \e /||| | | \e /| | | \ x / | \e /| | | | | \e /||| | \ x / | \e /| | | | \e /|| | | \e /|| | | | \e /||| | | \e /| | | \ x / | \e /| |
x 3*e 2*e 3*e 4*cos (x) 4*cos(x) \ sin (x) sin (x) / \ sin (x)/ \ sin (x)/ \ \sin\x /// \ sin \x / sin\x / sin\x / sin\x / x*sin\x / / \sin\x // \ \sin\x /// \ sin\x / / \ sin\x / / \sin\x // \ \sin\x /// \ sin\x / / \sin\x // \ \sin\x /// \ \sin\x /// \ sin\x / / \sin\x // \ \sin\x /// \ sin\x / / \ sin\x / / \ \sin\x /// \ sin\x / / \sin\x // \sin\x // \ \sin\x /// \ sin\x / / \ sin\x / /
e *log(x) - ---- + ---- + ---- + --------- + -------- - ------------------------------------ - ----------------------- + ---------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------ + ------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
2 3 x 3 sin(x) cos(x) 3 cos(x) / / sinh(x)\\ / / sinh(x)\\ / / sinh(x)\\ / / sinh(x)\\ / / sinh(x)\\ / / sinh(x)\\ / / sinh(x)\\ / / sinh(x)\\
x x sin (x) cos (x) 2| \e /| 2 2| \e /| 2 3| \e /| 2 2| \e /| 2 3| \e /| 3| \e /| 2| \e /| 3| \e /|
sin \x / x *sin \x / x *sin \x / x *sin \x / x *sin \x / x*sin \x / x*sin \x / x*sin \x /
$$- \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(\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{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{\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{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) \tanh{\left(\frac{1}{\sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}} \right)}}{\sin^{2}{\left(x^{e^{\sinh{\left(x \right)}}} \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 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(\tanh^{2}{\left(\frac{1}{\sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}} \right)} - 1\right)^{2} \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)}}}{x \sin^{3}{\left(x^{e^{\sinh{\left(x \right)}}} \right)}} - \frac{12 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(\tanh^{2}{\left(\frac{1}{\sin{\left(x^{e^{\sinh{\left(x \right)}}} \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^{2}{\left(\frac{1}{\sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}} \right)}}{x \sin^{3}{\left(x^{e^{\sinh{\left(x \right)}}} \right)}} - \frac{6 x^{e^{\sinh{\left(x \right)}}} \left(\tanh^{2}{\left(\frac{1}{\sin{\left(x^{e^{\sinh{\left(x \right)}}} \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^{2}{\left(x^{e^{\sinh{\left(x \right)}}} \right)}} + \frac{3 e^{x}}{x} + \frac{16 \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)^{2} \tanh{\left(\frac{1}{\sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}} \right)}}{x^{2} \sin^{3}{\left(x^{e^{\sinh{\left(x \right)}}} \right)}} + \frac{8 \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) \tanh^{3}{\left(\frac{1}{\sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}} \right)}}{x^{2} \sin^{3}{\left(x^{e^{\sinh{\left(x \right)}}} \right)}} + \frac{6 \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} \left(\tanh^{2}{\left(\frac{1}{\sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}} \right)} - 1\right)^{2}}{x^{2} \sin^{2}{\left(x^{e^{\sinh{\left(x \right)}}} \right)}} + \frac{12 \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} \left(\tanh^{2}{\left(\frac{1}{\sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}} \right)} - 1\right) \tanh^{2}{\left(\frac{1}{\sin{\left(x^{e^{\sinh{\left(x \right)}}} \right)}} \right)}}{x^{2} \sin^{2}{\left(x^{e^{\sinh{\left(x \right)}}} \right)}} - \frac{3 e^{x}}{x^{2}} + \frac{2 e^{x}}{x^{3}}$$