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 1/(x+3)
-
Derivada de 4*y
-
Derivada de (-1)/x-3*x
-
Derivada de y=csc(3x²+1)
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Expresiones idénticas
- x*tanh(x/(x*sin(x^(exp))))/(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 )))) 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))))/(log(xexp(x))+log(cos(x)/sin(x)))
- x*tanhx/x*sinxexp/logxexpx+logcosx/sinx
- xtanh(x/(xsin(x^(exp))))/(log(x^exp(x))+log(cos(x)/sin(x)))
- xtanh(x/(xsin(x(exp))))/(log(xexp(x))+log(cos(x)/sin(x)))
- xtanhx/xsinxexp/logxexpx+logcosx/sinx
- xtanhx/xsinx^exp/logx^expx+logcosx/sinx
- x*tanh(x dividir por (x*sin(x^(exp)))) dividir por (log(x^exp(x))+log(cos(x) dividir por sin(x)))
-
Expresiones semejantes
- x*tanh(x/(x*sin(x^(exp))))/(log(x^exp(x))-log(cos(x)/sin(x)))
- x*tanh(x/(x*sin(x^(exp))))/(log(x^exp(x))+log(cosx/sinx))
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Expresiones con funciones
- Seno sin
- sin(x+π)
- sin(x)^(2)*2^x^2
- sin^n(x)
- sin(x)^(32)*cos(8*x)^5
- sin(7*x)^(2)
- Logaritmo log
- log(1)
- log(acos(1/sqrt(x)))
- log(x+1)+1
- log(6+6/x)
- log(4+3*x)
- Logaritmo log
- log(1)
- log(acos(1/sqrt(x)))
- log(x+1)+1
- log(6+6/x)
- log(4+3*x)
- Coseno cos
- cos(log(x))+x^2*tan(x)
- cos(-6x+7)
- cos(3*x)/3
- cos(2*x+pi/3)
- cos(2-3*x)
- Seno sin
- sin(x+π)
- sin(x)^(2)*2^x^2
- sin^n(x)
- sin(x)^(32)*cos(8*x)^5
- sin(7*x)^(2)
Derivada de x*tanh(x/(x*sin(x^(exp))))/(log(x^exp(x))+log(cos(x)/sin(x)))
Solución
Ha introducido
[src]
/ x \
x*tanh|------------|
| / / x\\|
| | \e /||
\x*sin\x //
------------------------
/ / x\\
| \e /| /cos(x)\
log\x / + log|------|
\sin(x)/
$$\frac{x \tanh{\left(\frac{x}{x \sin{\left(x^{e^{x}} \right)}} \right)}}{\log{\left(x^{e^{x}} \right)} + \log{\left(\frac{\cos{\left(x \right)}}{\sin{\left(x \right)}} \right)}}$$
(x*tanh(x/((x*sin(x^exp(x))))))/(log(x^exp(x)) + log(cos(x)/sin(x)))
Primera derivada
[src]
/ / 2 \ \
/ / / x\\ / x\ / x \ / / x\\\ | | cos (x)| |
| | \e /| \e / |e x | | \e /|| | |-1 - -------|*sin(x)|
| - sin\x / - x*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|------------|
| | / / x\\|| | / / x\\ / / x\\ | | / / x\\| \ x cos(x) / | / / 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)//
$$\frac{x \left(- \frac{\left(-1 - \frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) \sin{\left(x \right)}}{\cos{\left(x \right)}} - e^{x} \log{\left(x \right)} - \frac{e^{x}}{x}\right) \tanh{\left(\frac{x}{x \sin{\left(x^{e^{x}} \right)}} \right)}}{\left(\log{\left(x^{e^{x}} \right)} + \log{\left(\frac{\cos{\left(x \right)}}{\sin{\left(x \right)}} \right)}\right)^{2}} + \frac{x \left(1 - \tanh^{2}{\left(\frac{x}{x \sin{\left(x^{e^{x}} \right)}} \right)}\right) \left(\frac{1}{x \sin{\left(x^{e^{x}} \right)}} + \frac{- x x^{e^{x}} \left(e^{x} \log{\left(x \right)} + \frac{e^{x}}{x}\right) \cos{\left(x^{e^{x}} \right)} - \sin{\left(x^{e^{x}} \right)}}{x \sin^{2}{\left(x^{e^{x}} \right)}}\right) + \tanh{\left(\frac{x}{x \sin{\left(x^{e^{x}} \right)}} \right)}}{\log{\left(x^{e^{x}} \right)} + \log{\left(\frac{\cos{\left(x \right)}}{\sin{\left(x \right)}} \right)}}$$
Segunda derivada
[src]
/ 2 \
| / / x\ / / x\\ / / x\\\ |
| | \e / /1 \ | \e /| x | \e /|| |
| | x*x *|- + log(x)|*cos\x /*e + sin\x /| |
| | \x / | / 1 \ | / 2 \
| / / / x\ / / x\\ / / x\\\ / / x\\ \ 2*|-1 + -----------------------------------------------| *tanh|----------| / / x\ / / x\\ / / x\\\| / / / x\ / / x\\ / / x\\\ \ | / / 2 \ \ |
| | /1 \ | \e / /1 \ | \e /| x | \e /|| | \e /| | | / / x\\ | | / / x\\| | \e / /1 \ | \e /| x | \e /||| | | \e / /1 \ | \e /| x | \e /|| | | | | cos (x)| | |
| / x\ | / / x\\ / / x\\ 2 / / x\\ 2*|- + log(x)|*|x*x *|- + log(x)|*cos\x /*e + sin\x /|*cos\x / / x\ 2 / / x\\| | | \e /| | | | \e /|| | x*x *|- + log(x)|*cos\x /*e + sin\x /|| | | x*x *|- + log(x)|*cos\x /*e + sin\x /| | | | |1 + -------|*sin(x)| / 2 \|
| \e / | /1 \ | \e /| / 1 2 \ | \e /| /1 \ | \e /| x \x / \ \x / / \e / /1 \ x | \e /|| x \ sin\x / / \sin\x // | \x / || |/ 2/ 1 \\ | \x / | | / / 2 \ \ | | x | 2 | | 2 | cos (x)||
|x *|2*|- + log(x)|*cos\x / + x*|- -- + - + log(x)|*cos\x / + x*|- + log(x)| *cos\x /*e - --------------------------------------------------------------------------- - x*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 / / / x\\ \x / | x | / / x\\ || || | / / x\\|| | / / 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 | | / / x\\|
| | / / x\\|| | / / x\\ x | | / / x\\ | / / 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)/ /
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------- - -----------------------------------------------------------------------------------------------------------------------------
/ / 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^{x}} \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^{x}} \left(- x x^{e^{x}} \left(\log{\left(x \right)} + \frac{1}{x}\right)^{2} e^{x} \sin{\left(x^{e^{x}} \right)} + x \left(\log{\left(x \right)} + \frac{1}{x}\right)^{2} e^{x} \cos{\left(x^{e^{x}} \right)} + x \left(\log{\left(x \right)} + \frac{2}{x} - \frac{1}{x^{2}}\right) \cos{\left(x^{e^{x}} \right)} - \frac{2 \left(x x^{e^{x}} \left(\log{\left(x \right)} + \frac{1}{x}\right) e^{x} \cos{\left(x^{e^{x}} \right)} + \sin{\left(x^{e^{x}} \right)}\right) \left(\log{\left(x \right)} + \frac{1}{x}\right) \cos{\left(x^{e^{x}} \right)}}{\sin{\left(x^{e^{x}} \right)}} + 2 \left(\log{\left(x \right)} + \frac{1}{x}\right) \cos{\left(x^{e^{x}} \right)}\right) e^{x} + \frac{2 \left(\frac{x x^{e^{x}} \left(\log{\left(x \right)} + \frac{1}{x}\right) e^{x} \cos{\left(x^{e^{x}} \right)} + \sin{\left(x^{e^{x}} \right)}}{\sin{\left(x^{e^{x}} \right)}} - 1\right)^{2} \tanh{\left(\frac{1}{\sin{\left(x^{e^{x}} \right)}} \right)}}{x}}{\sin{\left(x^{e^{x}} \right)}} + \frac{2 \left(\frac{x x^{e^{x}} \left(\log{\left(x \right)} + \frac{1}{x}\right) e^{x} \cos{\left(x^{e^{x}} \right)} + \sin{\left(x^{e^{x}} \right)}}{\sin{\left(x^{e^{x}} \right)}} - 1\right)}{x}\right) \left(\tanh^{2}{\left(\frac{1}{\sin{\left(x^{e^{x}} \right)}} \right)} - 1\right)}{\sin{\left(x^{e^{x}} \right)}} - \frac{2 \left(\frac{\left(\frac{x x^{e^{x}} \left(\log{\left(x \right)} + \frac{1}{x}\right) e^{x} \cos{\left(x^{e^{x}} \right)} + \sin{\left(x^{e^{x}} \right)}}{\sin{\left(x^{e^{x}} \right)}} - 1\right) \left(\tanh^{2}{\left(\frac{1}{\sin{\left(x^{e^{x}} \right)}} \right)} - 1\right)}{\sin{\left(x^{e^{x}} \right)}} + \tanh{\left(\frac{1}{\sin{\left(x^{e^{x}} \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 \
| | / / x\ / / x\\ / / x\\\ | | | / / x\ / / x\\ / / x\\\ |
| | | \e / /1 \ | \e /| x | \e /|| | | | | \e / /1 \ | \e /| x | \e /|| |
| | | x*x *|- + log(x)|*cos\x /*e + sin\x /| | | / 3 / / 2 \ \ / / 2 \\ \ | | x*x *|- + log(x)|*cos\x /*e + sin\x /| |
| | | \x / | / 1 \| 3 3 | / / / x\ / / x\\ / / x\\\ \ / 2 \ | / / 2 \ \ | | cos (x)| | | 2 | cos (x)|| | | | \x / | / 1 \ |
| | / / / x\ / / x\\ / / x\\\ / / x\\ \ 2*|-1 + -----------------------------------------------| *tanh|----------|| / / x\ / / x\\ \ / / x\ / / x\\ / / x\\\ / / x\ / / x\\ / / x\\\ / / x\ / / x\\ / / x\\\ / / / x\ / / x\\ / / x\\\ / / x\\ \ | | | \e / /1 \ | \e /| x | \e /|| | | / / 2 \ \ | | | | cos (x)| | | |1 + -------|*sin(x)| | sin (x)*|1 + -------|| | | / / / x\ / / x\\ / / x\\\ / / x\\ \ 2*|-1 + -----------------------------------------------| *tanh|----------| / / x\ / / x\\ / / x\\\|
| | | /1 \ | \e / /1 \ | \e /| x | \e /|| | \e /| | | / / x\\ | | / / x\\|| | \e / /1 \ | \e /| x| | \e / /1 \ | \e /| x | \e /|| | \e / /1 \ | \e /| x | \e /|| | \e / /1 \ | \e /| x | \e /|| | /1 \ | \e / /1 \ | \e /| x | \e /|| | \e /| | | | | x*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 /| x | \e /|| | \e /| | | / / x\\ | | / / x\\| | \e / /1 \ | \e /| x | \e /|||
| | / x\ | / / x\\ / / x\\ 2 / / x\\ 2*|- + log(x)|*|x*x *|- + log(x)|*cos\x /*e + sin\x /|*cos\x / / x\ 2 / / x\\| | | \e /| | | | \e /||| | x *|- + log(x)|*cos\x /*e | / / x\ / / x\\ / / x\\\ | x*x *|- + log(x)|*cos\x /*e + sin\x /| | x*x *|- + log(x)|*cos\x /*e + sin\x /| / x\ | x*x *|- + log(x)|*cos\x /*e + sin\x /| | / / x\\ / / x\\ 2 / / x\\ 2*|- + log(x)|*|x*x *|- + log(x)|*cos\x /*e + sin\x /|*cos\x / / x\ 2 / / 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)| | | / x\ | / / x\\ / / x\\ 2 / / x\\ 2*|- + log(x)|*|x*x *|- + log(x)|*cos\x /*e + sin\x /|*cos\x / / x\ 2 / / x\\| | | \e /| | | | \e /|| | x*x *|- + log(x)|*cos\x /*e + sin\x /||
| | \e / | /1 \ | \e /| / 1 2 \ | \e /| /1 \ | \e /| x \x / \ \x / / \e / /1 \ x | \e /|| x \ sin\x / / \sin\x //| |1 \x / | | \e / /1 \ | \e /| x | \e /|| / x\ / / / x\\ / / x\\ 2 / / x\\ / x\ 2 / / x\\\ | \x / | / 2/ 1 \\ | \x / | 2/ 1 \ x / / / x\\ / / x\\ 2 / / x\\ / x\ 2 / / x\\\ / / x\\ / x\ / / x\ / / x\\ / / x\\\ / / x\\ \e / | \x / | | /1 \ | \e /| / 1 2 \ | \e /| /1 \ | \e /| x \x / \ \x / / \e / /1 \ x | \e /|| 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 \ | \e /| /1 \ | \e /| x \x / \ \x / / \e / /1 \ x | \e /|| x \ sin\x / / \sin\x // | \x / || / / 2 \ \
| / x\ / / x\\ / / x\\ 3*|x *|2*|- + log(x)|*cos\x / + x*|- -- + - + log(x)|*cos\x / + x*|- + log(x)| *cos\x /*e - --------------------------------------------------------------------------- - x*x *|- + log(x)| *e *sin\x /|*e + --------------------------------------------------------------------------| |- + --------------------------------|*|x*x *|- + log(x)|*cos\x /*e + sin\x /| \e / | /1 \ | \e /| / 1 2 \ | \e /| /1 \ | \e /| x \e / /1 \ x | \e /|| x 2*|-1 + -----------------------------------------------| *|-1 + tanh |----------|| 4*|-1 + -----------------------------------------------| *tanh |----------| 2*e /1 \ | /1 \ | \e /| / 1 2 \ | \e /| /1 \ | \e /| x \e / /1 \ x | \e /|| | \e /| 2*x / x\ 2 / / x\ / / x\\ / / x\\\ / / x\\ \e / | \e / /1 \ | \e /| x | \e /|| / 1 2 \ | \e /| x x 2 / / x\\ / / x\ / / x\\ / / x\\\ / x\ / / x\ / / x\\ / / x\\\ / / x\\ 6*x *|-1 + -----------------------------------------------|*|2*|- + log(x)|*cos\x / + x*|- -- + - + log(x)|*cos\x / + x*|- + log(x)| *cos\x /*e - --------------------------------------------------------------------------- - x*x *|- + log(x)| *e *sin\x /|*e *tanh|----------|| || | / / x\\|| | / / 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*|- + log(x)|*cos\x / + x*|- -- + - + log(x)|*cos\x / + x*|- + log(x)| *cos\x /*e - --------------------------------------------------------------------------- - x*x *|- + log(x)| *e *sin\x /|*e + -------------------------------------------------------------------------- 2*|-1 + -----------------------------------------------|| | | cos (x)| |
| \e / /1 \ | \e /| x | \e /| | | \x / | 2 x | \x / / / x\\ \x / | x | |x / / x\\ | \ \x / / x *|2*|- + log(x)|*cos\x / + x*|- -- + - + log(x)|*cos\x / + x*|- + log(x)| *cos\x /*e - x*x *|- + log(x)| *e *sin\x /|*e | / / x\\ | | | / / x\\|| | / / x\\ | | / / x\\| 4*x *|- + log(x)|*|2*|- + log(x)|*cos\x / + x*|- -- + - + log(x)|*cos\x / + x*|- + log(x)| *cos\x /*e - x*x *|- + log(x)| *e *sin\x /|*cos\x /*e \e / /1 \ | \e / /1 \ | \e /| x | \e /|| | \e /| 2*x 2*x *|x*x *|- + log(x)|*cos\x /*e + sin\x /|*|- -- + - + log(x)|*cos\x /*e 2*e /1 \ 2| \e /| | \e / /1 \ | \e /| x | \e /|| 2*x \e / /1 \ | \e / /1 \ | \e /| x | \e /|| | \e /| x | / / x\\ | | \x / | 2 x | \x / / / x\\ \x / | | / / 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 / / / x\\ \x / | x | / / x\\ || | |1 + -------|*sin(x)|
|x*x *|- + log(x)|*cos\x /*e + sin\x / | | \ x / | \e /| | | / x\ / / / x\\ / / x\\ 2 / / x\\ 3 / / x\\ / x\ 2 / / x\\ x 3 / / x\\ / x\ 3 / / x\\ / / x\\ / x\ / / x\\\ | | \e /| | | \x / | 2 x | \x / \x / | | | \e /| | | | | \e /||| x 2 / / x\ / / x\\ / / x\\\ | | \e /| | | | \e /|| \x / | \x / | 2 x | \x / \x / | 2*x *|- + log(x)| *|x*x *|- + log(x)|*cos\x /*e + sin\x /|*cos\x /*e \ \x / / | 2 x | 6*x *|- + log(x)| *cos \x /*|x*x *|- + log(x)|*cos\x /*e + sin\x /|*e 3*x *|- + log(x)|*|x*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 \ | \e /| / 3 2 3 \ | \e /| /1 \ | \e /| x /1 \ | \e /| 2*x \e / /1 \ x | \e /| 2*e /1 \ | \e /| 2*x \e / /1 \ 2*x | \e /| /1 \ / 1 2 \ | \e /| x \e / /1 \ / 1 2 \ x | \e /|| x \ sin\x / / \ \ x / / \ sin\x / / \ \sin\x /// 2*e /1 \ | \e / /1 \ | \e /| x | \e /|| 2*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) | | / / x\\| / 2/ 1 \\ | \ sin\x / / \ sin\x / /| |e x \ sin (x)/ |
|-1 + tanh |----------||*|----------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + x *|3*|- -- + - + log(x)|*cos\x / + x*|- -- + -- + - + log(x)|*cos\x / + 3*|- + log(x)| *cos\x /*e + x*|- + log(x)| *cos\x /*e - 3*x *|- + log(x)| *e *sin\x / - x*x *|- + log(x)| *cos\x /*e - 3*x*x *|- + log(x)| *e *sin\x / + 3*x*|- + log(x)|*|- -- + - + log(x)|*cos\x /*e - 3*x*x *|- + log(x)|*|- -- + - + log(x)|*e *sin\x /|*e - ---------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------- + 2*x *|- + log(x)| *|x*x *|- + log(x)|*cos\x /*e + sin\x /|*e + --------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------ + -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| | / / x\\ | / / x\\|| | 2 2 / / x\\ x 2 | | x x sin (x) / / / x\\ \ | \e /| /cos(x)\ cos (x) | | | \e /|| 3*|-1 + tanh |----------||*|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------|*|-- + e *log(x) - --------------------|
| | / / x\\|| | 2 x | | 2 x | | 2 3 x | \x / \x / \x / \x / \x / \x / | 2 x | \x / | 2 x | | x x / / x\\ \x / \ \x / / / / x\\ / / x\\ / / x\\ / / x\\ / / x\\ / / x\\ / / x\\ | | | \e /| | | \e /||| | sin (x) x | \e /| /cos(x)\ cos (x) | | | | \e /| /cos(x)\| log\x / + log|------| | \sin\x // | | / / x\\|| | / / 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 / /
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
/ / x\\ / / x\\ / / x\\ / / / x\\ \ / / 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^{x}} \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^{x}} \left(- x x^{e^{x}} \left(\log{\left(x \right)} + \frac{1}{x}\right)^{2} e^{x} \sin{\left(x^{e^{x}} \right)} + x \left(\log{\left(x \right)} + \frac{1}{x}\right)^{2} e^{x} \cos{\left(x^{e^{x}} \right)} + x \left(\log{\left(x \right)} + \frac{2}{x} - \frac{1}{x^{2}}\right) \cos{\left(x^{e^{x}} \right)} - \frac{2 \left(x x^{e^{x}} \left(\log{\left(x \right)} + \frac{1}{x}\right) e^{x} \cos{\left(x^{e^{x}} \right)} + \sin{\left(x^{e^{x}} \right)}\right) \left(\log{\left(x \right)} + \frac{1}{x}\right) \cos{\left(x^{e^{x}} \right)}}{\sin{\left(x^{e^{x}} \right)}} + 2 \left(\log{\left(x \right)} + \frac{1}{x}\right) \cos{\left(x^{e^{x}} \right)}\right) e^{x} + \frac{2 \left(\frac{x x^{e^{x}} \left(\log{\left(x \right)} + \frac{1}{x}\right) e^{x} \cos{\left(x^{e^{x}} \right)} + \sin{\left(x^{e^{x}} \right)}}{\sin{\left(x^{e^{x}} \right)}} - 1\right)^{2} \tanh{\left(\frac{1}{\sin{\left(x^{e^{x}} \right)}} \right)}}{x}}{\sin{\left(x^{e^{x}} \right)}} + \frac{2 \left(\frac{x x^{e^{x}} \left(\log{\left(x \right)} + \frac{1}{x}\right) e^{x} \cos{\left(x^{e^{x}} \right)} + \sin{\left(x^{e^{x}} \right)}}{\sin{\left(x^{e^{x}} \right)}} - 1\right)}{x}\right) \left(\tanh^{2}{\left(\frac{1}{\sin{\left(x^{e^{x}} \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^{x}} \right)}} - \frac{3 \left(\frac{\left(\frac{x x^{e^{x}} \left(\log{\left(x \right)} + \frac{1}{x}\right) e^{x} \cos{\left(x^{e^{x}} \right)} + \sin{\left(x^{e^{x}} \right)}}{\sin{\left(x^{e^{x}} \right)}} - 1\right) \left(\tanh^{2}{\left(\frac{1}{\sin{\left(x^{e^{x}} \right)}} \right)} - 1\right)}{\sin{\left(x^{e^{x}} \right)}} + \tanh{\left(\frac{1}{\sin{\left(x^{e^{x}} \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^{x}} \right)}} \right)} - 1\right) \left(2 x^{2 e^{x}} \left(x x^{e^{x}} \left(\log{\left(x \right)} + \frac{1}{x}\right) e^{x} \cos{\left(x^{e^{x}} \right)} + \sin{\left(x^{e^{x}} \right)}\right) \left(\log{\left(x \right)} + \frac{1}{x}\right)^{2} e^{2 x} + \frac{6 x^{2 e^{x}} \left(x x^{e^{x}} \left(\log{\left(x \right)} + \frac{1}{x}\right) e^{x} \cos{\left(x^{e^{x}} \right)} + \sin{\left(x^{e^{x}} \right)}\right) \left(\log{\left(x \right)} + \frac{1}{x}\right)^{2} e^{2 x} \cos^{2}{\left(x^{e^{x}} \right)}}{\sin^{2}{\left(x^{e^{x}} \right)}} - \frac{4 x^{2 e^{x}} \left(\log{\left(x \right)} + \frac{1}{x}\right) \left(- x x^{e^{x}} \left(\log{\left(x \right)} + \frac{1}{x}\right)^{2} e^{x} \sin{\left(x^{e^{x}} \right)} + x \left(\log{\left(x \right)} + \frac{1}{x}\right)^{2} e^{x} \cos{\left(x^{e^{x}} \right)} + x \left(\log{\left(x \right)} + \frac{2}{x} - \frac{1}{x^{2}}\right) \cos{\left(x^{e^{x}} \right)} + 2 \left(\log{\left(x \right)} + \frac{1}{x}\right) \cos{\left(x^{e^{x}} \right)}\right) e^{2 x} \cos{\left(x^{e^{x}} \right)}}{\sin{\left(x^{e^{x}} \right)}} - \frac{2 x^{e^{x}} \left(x x^{e^{x}} \left(\log{\left(x \right)} + \frac{1}{x}\right) e^{x} \cos{\left(x^{e^{x}} \right)} + \sin{\left(x^{e^{x}} \right)}\right) \left(\log{\left(x \right)} + \frac{1}{x}\right)^{2} e^{2 x} \cos{\left(x^{e^{x}} \right)}}{\sin{\left(x^{e^{x}} \right)}} - \frac{2 x^{e^{x}} \left(x x^{e^{x}} \left(\log{\left(x \right)} + \frac{1}{x}\right) e^{x} \cos{\left(x^{e^{x}} \right)} + \sin{\left(x^{e^{x}} \right)}\right) \left(\log{\left(x \right)} + \frac{2}{x} - \frac{1}{x^{2}}\right) e^{x} \cos{\left(x^{e^{x}} \right)}}{\sin{\left(x^{e^{x}} \right)}} + x^{e^{x}} \left(- x x^{2 e^{x}} \left(\log{\left(x \right)} + \frac{1}{x}\right)^{3} e^{2 x} \cos{\left(x^{e^{x}} \right)} - 3 x x^{e^{x}} \left(\log{\left(x \right)} + \frac{1}{x}\right)^{3} e^{2 x} \sin{\left(x^{e^{x}} \right)} - 3 x x^{e^{x}} \left(\log{\left(x \right)} + \frac{1}{x}\right) \left(\log{\left(x \right)} + \frac{2}{x} - \frac{1}{x^{2}}\right) e^{x} \sin{\left(x^{e^{x}} \right)} + x \left(\log{\left(x \right)} + \frac{1}{x}\right)^{3} e^{2 x} \cos{\left(x^{e^{x}} \right)} + 3 x \left(\log{\left(x \right)} + \frac{1}{x}\right) \left(\log{\left(x \right)} + \frac{2}{x} - \frac{1}{x^{2}}\right) e^{x} \cos{\left(x^{e^{x}} \right)} + x \left(\log{\left(x \right)} + \frac{3}{x} - \frac{3}{x^{2}} + \frac{2}{x^{3}}\right) \cos{\left(x^{e^{x}} \right)} - 3 x^{e^{x}} \left(\log{\left(x \right)} + \frac{1}{x}\right)^{2} e^{x} \sin{\left(x^{e^{x}} \right)} + 3 \left(\log{\left(x \right)} + \frac{1}{x}\right)^{2} e^{x} \cos{\left(x^{e^{x}} \right)} + 3 \left(\log{\left(x \right)} + \frac{2}{x} - \frac{1}{x^{2}}\right) \cos{\left(x^{e^{x}} \right)}\right) e^{x} + \frac{6 x^{e^{x}} \left(\frac{x x^{e^{x}} \left(\log{\left(x \right)} + \frac{1}{x}\right) e^{x} \cos{\left(x^{e^{x}} \right)} + \sin{\left(x^{e^{x}} \right)}}{\sin{\left(x^{e^{x}} \right)}} - 1\right) \left(- x x^{e^{x}} \left(\log{\left(x \right)} + \frac{1}{x}\right)^{2} e^{x} \sin{\left(x^{e^{x}} \right)} + x \left(\log{\left(x \right)} + \frac{1}{x}\right)^{2} e^{x} \cos{\left(x^{e^{x}} \right)} + x \left(\log{\left(x \right)} + \frac{2}{x} - \frac{1}{x^{2}}\right) \cos{\left(x^{e^{x}} \right)} - \frac{2 \left(x x^{e^{x}} \left(\log{\left(x \right)} + \frac{1}{x}\right) e^{x} \cos{\left(x^{e^{x}} \right)} + \sin{\left(x^{e^{x}} \right)}\right) \left(\log{\left(x \right)} + \frac{1}{x}\right) \cos{\left(x^{e^{x}} \right)}}{\sin{\left(x^{e^{x}} \right)}} + 2 \left(\log{\left(x \right)} + \frac{1}{x}\right) \cos{\left(x^{e^{x}} \right)}\right) e^{x} \tanh{\left(\frac{1}{\sin{\left(x^{e^{x}} \right)}} \right)}}{x \sin{\left(x^{e^{x}} \right)}} + \frac{3 x^{e^{x}} \left(x x^{e^{x}} \left(\log{\left(x \right)} + \frac{1}{x}\right) e^{x} \cos{\left(x^{e^{x}} \right)} + \sin{\left(x^{e^{x}} \right)}\right) \left(\log{\left(x \right)} + \frac{1}{x}\right) e^{x} \cos{\left(x^{e^{x}} \right)}}{x \sin{\left(x^{e^{x}} \right)}} - \frac{x^{e^{x}} \left(- x x^{e^{x}} \left(\log{\left(x \right)} + \frac{1}{x}\right)^{2} e^{x} \sin{\left(x^{e^{x}} \right)} + x \left(\log{\left(x \right)} + \frac{1}{x}\right)^{2} e^{x} \cos{\left(x^{e^{x}} \right)} + x \left(\log{\left(x \right)} + \frac{2}{x} - \frac{1}{x^{2}}\right) \cos{\left(x^{e^{x}} \right)} + 2 \left(\log{\left(x \right)} + \frac{1}{x}\right) \cos{\left(x^{e^{x}} \right)}\right) e^{x}}{x} + \frac{3 \left(x^{e^{x}} \left(- x x^{e^{x}} \left(\log{\left(x \right)} + \frac{1}{x}\right)^{2} e^{x} \sin{\left(x^{e^{x}} \right)} + x \left(\log{\left(x \right)} + \frac{1}{x}\right)^{2} e^{x} \cos{\left(x^{e^{x}} \right)} + x \left(\log{\left(x \right)} + \frac{2}{x} - \frac{1}{x^{2}}\right) \cos{\left(x^{e^{x}} \right)} - \frac{2 \left(x x^{e^{x}} \left(\log{\left(x \right)} + \frac{1}{x}\right) e^{x} \cos{\left(x^{e^{x}} \right)} + \sin{\left(x^{e^{x}} \right)}\right) \left(\log{\left(x \right)} + \frac{1}{x}\right) \cos{\left(x^{e^{x}} \right)}}{\sin{\left(x^{e^{x}} \right)}} + 2 \left(\log{\left(x \right)} + \frac{1}{x}\right) \cos{\left(x^{e^{x}} \right)}\right) e^{x} + \frac{2 \left(\frac{x x^{e^{x}} \left(\log{\left(x \right)} + \frac{1}{x}\right) e^{x} \cos{\left(x^{e^{x}} \right)} + \sin{\left(x^{e^{x}} \right)}}{\sin{\left(x^{e^{x}} \right)}} - 1\right)^{2} \tanh{\left(\frac{1}{\sin{\left(x^{e^{x}} \right)}} \right)}}{x}\right)}{x} - \frac{\left(x x^{e^{x}} \left(\log{\left(x \right)} + \frac{1}{x}\right) e^{x} \cos{\left(x^{e^{x}} \right)} + \sin{\left(x^{e^{x}} \right)}\right) \left(\frac{x^{e^{x}} \left(\log{\left(x \right)} + \frac{1}{x}\right) e^{x} \cos{\left(x^{e^{x}} \right)}}{\sin{\left(x^{e^{x}} \right)}} + \frac{1}{x}\right)}{x} + \frac{2 \left(\frac{x x^{e^{x}} \left(\log{\left(x \right)} + \frac{1}{x}\right) e^{x} \cos{\left(x^{e^{x}} \right)} + \sin{\left(x^{e^{x}} \right)}}{\sin{\left(x^{e^{x}} \right)}} - 1\right)^{3} \left(\tanh^{2}{\left(\frac{1}{\sin{\left(x^{e^{x}} \right)}} \right)} - 1\right)}{x^{2} \sin{\left(x^{e^{x}} \right)}} + \frac{4 \left(\frac{x x^{e^{x}} \left(\log{\left(x \right)} + \frac{1}{x}\right) e^{x} \cos{\left(x^{e^{x}} \right)} + \sin{\left(x^{e^{x}} \right)}}{\sin{\left(x^{e^{x}} \right)}} - 1\right)^{3} \tanh^{2}{\left(\frac{1}{\sin{\left(x^{e^{x}} \right)}} \right)}}{x^{2} \sin{\left(x^{e^{x}} \right)}} + \frac{x x^{e^{x}} \left(\log{\left(x \right)} + \frac{1}{x}\right) e^{x} \cos{\left(x^{e^{x}} \right)} + \sin{\left(x^{e^{x}} \right)}}{x^{2}}\right)}{\sin^{2}{\left(x^{e^{x}} \right)}}}{\log{\left(x^{e^{x}} \right)} + \log{\left(\frac{\cos{\left(x \right)}}{\sin{\left(x \right)}} \right)}}$$