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:
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Derivada de e^x*sin(x)
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Derivada de x*e^(1/x)
- Derivada de x!
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Derivada de e^y
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Expresiones idénticas
- y=sqrt(xcosxsqrt(uno -e^x))
- y es igual a raíz cuadrada de (x coseno de x raíz cuadrada de (1 menos e en el grado x))
- y es igual a raíz cuadrada de (x coseno de x raíz cuadrada de (uno menos e en el grado x))
- y=√(xcosx√(1-e^x))
- y=sqrt(xcosxsqrt(1-ex))
- y=sqrtxcosxsqrt1-ex
- y=sqrtxcosxsqrt1-e^x
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Expresiones semejantes
- y=sqrt(xcosxsqrt(1+e^x))
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Expresiones con funciones
- Raíz cuadrada sqrt
- sqrt(x-1)/(sqrt(x^2)-x-1)
- sqrt(x)/(x+1)
- sqrt(x)+1
- sqrt(ln(x))
- sqrt(x)*cos^5*(3x)
Derivada de y=sqrt(xcosxsqrt(1-e^x))
Solución
Ha introducido
[src]
______________________ / ________ / / x \/ x*cos(x)*\/ 1 - E
$$\sqrt{x \cos{\left(x \right)} \sqrt{1 - e^{x}}}$$
sqrt((x*cos(x))*sqrt(1 - E^x))
Solución detallada
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Sustituimos .
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Según el principio, aplicamos: tenemos
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Luego se aplica una cadena de reglas. Multiplicamos por :
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Se aplica la regla de la derivada de una multiplicación:
; calculamos :
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Se aplica la regla de la derivada de una multiplicación:
; calculamos :
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Según el principio, aplicamos: tenemos
; calculamos :
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La derivada del coseno es igual a menos el seno:
Como resultado de:
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; calculamos :
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Sustituimos .
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Según el principio, aplicamos: tenemos
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Luego se aplica una cadena de reglas. Multiplicamos por :
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diferenciamos miembro por miembro:
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La derivada de una constante es igual a cero.
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La derivada del producto de una constante por función es igual al producto de esta constante por la derivada de esta función.
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Derivado es.
Entonces, como resultado:
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Como resultado de:
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Como resultado de la secuencia de reglas:
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Como resultado de:
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Como resultado de la secuencia de reglas:
Simplificamos:
Respuesta:
Primera derivada
[src]
______________________ / ________ \
/ ________ | / x x |
/ / x |\/ 1 - E *(-x*sin(x) + cos(x)) x*cos(x)*e |
\/ x*\/ 1 - E *cos(x) *|-------------------------------- - -------------|
| 2 ________|
| / x |
\ 4*\/ 1 - E /
-----------------------------------------------------------------------------
________
/ x
x*\/ 1 - E *cos(x)
$$\frac{\sqrt{x \sqrt{1 - e^{x}} \cos{\left(x \right)}} \left(- \frac{x e^{x} \cos{\left(x \right)}}{4 \sqrt{1 - e^{x}}} + \frac{\sqrt{1 - e^{x}} \left(- x \sin{\left(x \right)} + \cos{\left(x \right)}\right)}{2}\right)}{x \sqrt{1 - e^{x}} \cos{\left(x \right)}}$$
Segunda derivada
[src]
/ / ________ x x 2*x x x\ / ________ x\ / ________ x\ / ________ x\ / ________ x\ / ________ ________ x\\
| | / x 2*(-cos(x) + x*sin(x))*e 2*cos(x)*e x*cos(x)*e 2*x*e *sin(x) 2*x*cos(x)*e | | / x x*cos(x)*e | x | / x x*cos(x)*e | | / x x*cos(x)*e | | / x x*cos(x)*e | | / x / x x*cos(x)*e ||
| 2*|4*\/ 1 - e *(2*sin(x) + x*cos(x)) - ------------------------- + ----------- + ------------- - ------------- + -------------| 2*|2*\/ 1 - e *(-cos(x) + x*sin(x)) + -----------|*e 4*|2*\/ 1 - e *(-cos(x) + x*sin(x)) + -----------| 4*|2*\/ 1 - e *(-cos(x) + x*sin(x)) + -----------|*sin(x) |2*\/ 1 - e *(-cos(x) + x*sin(x)) + -----------|*|- 2*\/ 1 - e *cos(x) + 2*x*\/ 1 - e *sin(x) + -----------||
______________________ | | ________ ________ 3/2 ________ ________ | | ________| | ________| | ________| | ________| | ________||
/ ________ | | / x / x / x\ / x / x | | / x | | / x | | / x | | / x | | / x ||
/ / x | \ \/ 1 - e \/ 1 - e \1 - e / \/ 1 - e \/ 1 - e / \ \/ 1 - e / \ \/ 1 - e / \ \/ 1 - e / \ \/ 1 - e / \ \/ 1 - e /|
\/ x*\/ 1 - e *cos(x) *|- --------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------- + ---------------------------------------------------- - ----------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------|
| ________ 3/2 ________ ________ / x\ |
| / x / x\ / x / x x*\-1 + e /*cos(x) |
\ \/ 1 - e \1 - e / x*\/ 1 - e \/ 1 - e *cos(x) /
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16*x*cos(x)
$$\frac{\sqrt{x \sqrt{1 - e^{x}} \cos{\left(x \right)}} \left(- \frac{4 \left(\frac{x e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}} + 2 \sqrt{1 - e^{x}} \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right)\right) \sin{\left(x \right)}}{\sqrt{1 - e^{x}} \cos{\left(x \right)}} - \frac{2 \left(- \frac{2 x e^{x} \sin{\left(x \right)}}{\sqrt{1 - e^{x}}} + \frac{2 x e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}} + \frac{x e^{2 x} \cos{\left(x \right)}}{\left(1 - e^{x}\right)^{\frac{3}{2}}} + 4 \sqrt{1 - e^{x}} \left(x \cos{\left(x \right)} + 2 \sin{\left(x \right)}\right) - \frac{2 \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right) e^{x}}{\sqrt{1 - e^{x}}} + \frac{2 e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}}\right)}{\sqrt{1 - e^{x}}} - \frac{2 \left(\frac{x e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}} + 2 \sqrt{1 - e^{x}} \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right)\right) e^{x}}{\left(1 - e^{x}\right)^{\frac{3}{2}}} - \frac{\left(\frac{x e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}} + 2 \sqrt{1 - e^{x}} \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right)\right) \left(2 x \sqrt{1 - e^{x}} \sin{\left(x \right)} + \frac{x e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}} - 2 \sqrt{1 - e^{x}} \cos{\left(x \right)}\right)}{x \left(e^{x} - 1\right) \cos{\left(x \right)}} + \frac{4 \left(\frac{x e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}} + 2 \sqrt{1 - e^{x}} \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right)\right)}{x \sqrt{1 - e^{x}}}\right)}{16 x \cos{\left(x \right)}}$$
Tercera derivada
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/ 2 \
| / ________ x\ / ________ x 2*x 2*x x x x 2*x 3*x 2*x x \ / ________ x\ / ________ x\ / ________ x\ / ________ x x 2*x x x\ / ________ x x 2*x x x\ / ________ x\ / ________ x x 2*x x x\ / ________ x\ / ________ ________ x\ / ________ x\ / ________ x\ / ________ ________ x\ / ________ x x 2*x x x\ / ________ x\ / ________ ________ x 2*x x x\ / ________ x\ / ________ ________ x\ / ________ x\ / ________ x\ / ________ ________ x\ / ________ x\ / ________ ________ x\ |
| | / x x*cos(x)*e | | / x 8*cos(x)*e 4*cos(x)*e 2*(-cos(x) + x*sin(x))*e 4*(-cos(x) + x*sin(x))*e 8*(2*sin(x) + x*cos(x))*e 8*e *sin(x) 6*x*cos(x)*e 3*x*cos(x)*e 4*x*e *sin(x) 8*x*e *sin(x)| | / x x*cos(x)*e | | / x x*cos(x)*e | 2*x | / x x*cos(x)*e | x | / x 2*(-cos(x) + x*sin(x))*e 2*cos(x)*e x*cos(x)*e 2*x*e *sin(x) 2*x*cos(x)*e | x | / x 2*(-cos(x) + x*sin(x))*e 2*cos(x)*e x*cos(x)*e 2*x*e *sin(x) 2*x*cos(x)*e | 2 | / x x*cos(x)*e | | / x 2*(-cos(x) + x*sin(x))*e 2*cos(x)*e x*cos(x)*e 2*x*e *sin(x) 2*x*cos(x)*e | | / x x*cos(x)*e | x | / x / x x*cos(x)*e | | / x x*cos(x)*e | | / x x*cos(x)*e | x | / x / x x*cos(x)*e | | / x 2*(-cos(x) + x*sin(x))*e 2*cos(x)*e x*cos(x)*e 2*x*e *sin(x) 2*x*cos(x)*e | | / x x*cos(x)*e | | / x / x 4*cos(x)*e x*cos(x)*e 4*x*e *sin(x) 2*x*cos(x)*e | | / x x*cos(x)*e | | / x / x x*cos(x)*e | | / x x*cos(x)*e | | / x x*cos(x)*e | | / x / x x*cos(x)*e | | / x x*cos(x)*e | | / x / x x*cos(x)*e | x|
| 16*|2*\/ 1 - e *(-cos(x) + x*sin(x)) + -----------| 4*|8*\/ 1 - e *(-3*cos(x) + x*sin(x)) - ----------- - ------------- + --------------------------- + ------------------------- + -------------------------- + ----------- - --------------- - --------------- + --------------- + -------------| 32*|2*\/ 1 - e *(-cos(x) + x*sin(x)) + -----------| 12*|2*\/ 1 - e *(-cos(x) + x*sin(x)) + -----------|*e 8*|2*\/ 1 - e *(-cos(x) + x*sin(x)) + -----------|*e 8*|4*\/ 1 - e *(2*sin(x) + x*cos(x)) - ------------------------- + ----------- + ------------- - ------------- + -------------|*e 16*|4*\/ 1 - e *(2*sin(x) + x*cos(x)) - ------------------------- + ----------- + ------------- - ------------- + -------------| 32*sin (x)*|2*\/ 1 - e *(-cos(x) + x*sin(x)) + -----------| 16*|4*\/ 1 - e *(2*sin(x) + x*cos(x)) - ------------------------- + ----------- + ------------- - ------------- + -------------|*sin(x) 16*|2*\/ 1 - e *(-cos(x) + x*sin(x)) + -----------|*e |- 2*\/ 1 - e *cos(x) + 2*x*\/ 1 - e *sin(x) + -----------| *|2*\/ 1 - e *(-cos(x) + x*sin(x)) + -----------| 16*|2*\/ 1 - e *(-cos(x) + x*sin(x)) + -----------|*e *sin(x) 4*|- 2*\/ 1 - e *cos(x) + 2*x*\/ 1 - e *sin(x) + -----------|*|4*\/ 1 - e *(2*sin(x) + x*cos(x)) - ------------------------- + ----------- + ------------- - ------------- + -------------| 2*|2*\/ 1 - e *(-cos(x) + x*sin(x)) + -----------|*|8*\/ 1 - e *sin(x) + 4*x*\/ 1 - e *cos(x) + ----------- + ------------- - ------------- + -------------| 12*|2*\/ 1 - e *(-cos(x) + x*sin(x)) + -----------|*|- 2*\/ 1 - e *cos(x) + 2*x*\/ 1 - e *sin(x) + -----------| 32*|2*\/ 1 - e *(-cos(x) + x*sin(x)) + -----------|*sin(x) 12*|2*\/ 1 - e *(-cos(x) + x*sin(x)) + -----------|*|- 2*\/ 1 - e *cos(x) + 2*x*\/ 1 - e *sin(x) + -----------|*sin(x) 6*|2*\/ 1 - e *(-cos(x) + x*sin(x)) + -----------|*|- 2*\/ 1 - e *cos(x) + 2*x*\/ 1 - e *sin(x) + -----------|*e |
______________________ | | ________| | ________ 3/2 3/2 ________ ________ ________ 3/2 5/2 3/2 ________ | | ________| | ________| | ________| | ________ ________ 3/2 ________ ________ | | ________ ________ 3/2 ________ ________ | | ________| | ________ ________ 3/2 ________ ________ | | ________| | ________| | ________| | ________| | ________| | ________ ________ 3/2 ________ ________ | | ________| | ________ 3/2 ________ ________ | | ________| | ________| | ________| | ________| | ________| | ________| | ________| |
/ ________ | | / x | | / x / x\ / x\ / x / x / x / x\ / x\ / x\ / x | | / x | | / x | | / x | | / x / x / x\ / x / x | | / x / x / x\ / x / x | | / x | | / x / x / x\ / x / x | | / x | | / x | | / x | | / x | | / x | | / x / x / x\ / x / x | | / x | | / x / x\ / x / x | | / x | | / x | | / x | | / x | | / x | | / x | | / x | |
/ / x | \ \/ 1 - e / \ \/ 1 - e \1 - e / \1 - e / \/ 1 - e \/ 1 - e \/ 1 - e \1 - e / \1 - e / \1 - e / \/ 1 - e / \ \/ 1 - e / \ \/ 1 - e / \ \/ 1 - e / \ \/ 1 - e \/ 1 - e \1 - e / \/ 1 - e \/ 1 - e / \ \/ 1 - e \/ 1 - e \1 - e / \/ 1 - e \/ 1 - e / \ \/ 1 - e / \ \/ 1 - e \/ 1 - e \1 - e / \/ 1 - e \/ 1 - e / \ \/ 1 - e / \ \/ 1 - e / \ \/ 1 - e / \ \/ 1 - e / \ \/ 1 - e / \ \/ 1 - e \/ 1 - e \1 - e / \/ 1 - e \/ 1 - e / \ \/ 1 - e / \ \/ 1 - e \1 - e / \/ 1 - e \/ 1 - e / \ \/ 1 - e / \ \/ 1 - e / \ \/ 1 - e / \ \/ 1 - e / \ \/ 1 - e / \ \/ 1 - e / \ \/ 1 - e / |
\/ x*\/ 1 - e *cos(x) *|- ----------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------- - ---------------------------------------------------------- - ------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------ + ---------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------ + --------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------ - ---------------------------------------------------------------------------------------------------------------------------- + -----------------------------------------------------------------------------------------------------------------------|
| ________ ________ ________ 5/2 3/2 3/2 ________ ________ ________ 3/2 3/2 3/2 / x\ / x\ 2 / x\ ________ / x\ 2 2 |
| / x / x 2 / x / x\ / x\ / x\ / x / x 2 / x / x\ 2 / x\ 2 / x\ x*\-1 + e /*cos(x) x*\-1 + e /*cos(x) x *\-1 + e /*cos(x) / x x*\-1 + e /*cos (x) / x\ |
\ \/ 1 - e \/ 1 - e x *\/ 1 - e \1 - e / \1 - e / \1 - e / x*\/ 1 - e \/ 1 - e *cos (x) \/ 1 - e *cos(x) x*\1 - e / x *\1 - e / *cos (x) \1 - e / *cos(x) x*\/ 1 - e *cos(x) x*\-1 + e / *cos(x) /
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64*x*cos(x)
$$\frac{\sqrt{x \sqrt{1 - e^{x}} \cos{\left(x \right)}} \left(- \frac{32 \left(\frac{x e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}} + 2 \sqrt{1 - e^{x}} \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right)\right) \sin^{2}{\left(x \right)}}{\sqrt{1 - e^{x}} \cos^{2}{\left(x \right)}} - \frac{16 \left(\frac{x e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}} + 2 \sqrt{1 - e^{x}} \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right)\right)}{\sqrt{1 - e^{x}}} - \frac{16 \left(- \frac{2 x e^{x} \sin{\left(x \right)}}{\sqrt{1 - e^{x}}} + \frac{2 x e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}} + \frac{x e^{2 x} \cos{\left(x \right)}}{\left(1 - e^{x}\right)^{\frac{3}{2}}} + 4 \sqrt{1 - e^{x}} \left(x \cos{\left(x \right)} + 2 \sin{\left(x \right)}\right) - \frac{2 \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right) e^{x}}{\sqrt{1 - e^{x}}} + \frac{2 e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}}\right) \sin{\left(x \right)}}{\sqrt{1 - e^{x}} \cos{\left(x \right)}} + \frac{4 \left(\frac{8 x e^{x} \sin{\left(x \right)}}{\sqrt{1 - e^{x}}} + \frac{4 x e^{2 x} \sin{\left(x \right)}}{\left(1 - e^{x}\right)^{\frac{3}{2}}} - \frac{6 x e^{2 x} \cos{\left(x \right)}}{\left(1 - e^{x}\right)^{\frac{3}{2}}} - \frac{3 x e^{3 x} \cos{\left(x \right)}}{\left(1 - e^{x}\right)^{\frac{5}{2}}} + 8 \sqrt{1 - e^{x}} \left(x \sin{\left(x \right)} - 3 \cos{\left(x \right)}\right) + \frac{4 \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right) e^{x}}{\sqrt{1 - e^{x}}} + \frac{8 \left(x \cos{\left(x \right)} + 2 \sin{\left(x \right)}\right) e^{x}}{\sqrt{1 - e^{x}}} + \frac{8 e^{x} \sin{\left(x \right)}}{\sqrt{1 - e^{x}}} - \frac{8 e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}} + \frac{2 \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right) e^{2 x}}{\left(1 - e^{x}\right)^{\frac{3}{2}}} - \frac{4 e^{2 x} \cos{\left(x \right)}}{\left(1 - e^{x}\right)^{\frac{3}{2}}}\right)}{\sqrt{1 - e^{x}}} - \frac{16 \left(\frac{x e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}} + 2 \sqrt{1 - e^{x}} \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right)\right) e^{x} \sin{\left(x \right)}}{\left(1 - e^{x}\right)^{\frac{3}{2}} \cos{\left(x \right)}} - \frac{8 \left(\frac{x e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}} + 2 \sqrt{1 - e^{x}} \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right)\right) e^{x}}{\left(1 - e^{x}\right)^{\frac{3}{2}}} - \frac{8 \left(- \frac{2 x e^{x} \sin{\left(x \right)}}{\sqrt{1 - e^{x}}} + \frac{2 x e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}} + \frac{x e^{2 x} \cos{\left(x \right)}}{\left(1 - e^{x}\right)^{\frac{3}{2}}} + 4 \sqrt{1 - e^{x}} \left(x \cos{\left(x \right)} + 2 \sin{\left(x \right)}\right) - \frac{2 \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right) e^{x}}{\sqrt{1 - e^{x}}} + \frac{2 e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}}\right) e^{x}}{\left(1 - e^{x}\right)^{\frac{3}{2}}} - \frac{12 \left(\frac{x e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}} + 2 \sqrt{1 - e^{x}} \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right)\right) e^{2 x}}{\left(1 - e^{x}\right)^{\frac{5}{2}}} - \frac{12 \left(\frac{x e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}} + 2 \sqrt{1 - e^{x}} \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right)\right) \left(2 x \sqrt{1 - e^{x}} \sin{\left(x \right)} + \frac{x e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}} - 2 \sqrt{1 - e^{x}} \cos{\left(x \right)}\right) \sin{\left(x \right)}}{x \left(e^{x} - 1\right) \cos^{2}{\left(x \right)}} - \frac{2 \left(\frac{x e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}} + 2 \sqrt{1 - e^{x}} \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right)\right) \left(4 x \sqrt{1 - e^{x}} \cos{\left(x \right)} - \frac{4 x e^{x} \sin{\left(x \right)}}{\sqrt{1 - e^{x}}} + \frac{2 x e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}} + \frac{x e^{2 x} \cos{\left(x \right)}}{\left(1 - e^{x}\right)^{\frac{3}{2}}} + 8 \sqrt{1 - e^{x}} \sin{\left(x \right)} + \frac{4 e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}}\right)}{x \left(e^{x} - 1\right) \cos{\left(x \right)}} + \frac{6 \left(\frac{x e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}} + 2 \sqrt{1 - e^{x}} \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right)\right) \left(2 x \sqrt{1 - e^{x}} \sin{\left(x \right)} + \frac{x e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}} - 2 \sqrt{1 - e^{x}} \cos{\left(x \right)}\right) e^{x}}{x \left(e^{x} - 1\right)^{2} \cos{\left(x \right)}} - \frac{4 \left(2 x \sqrt{1 - e^{x}} \sin{\left(x \right)} + \frac{x e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}} - 2 \sqrt{1 - e^{x}} \cos{\left(x \right)}\right) \left(- \frac{2 x e^{x} \sin{\left(x \right)}}{\sqrt{1 - e^{x}}} + \frac{2 x e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}} + \frac{x e^{2 x} \cos{\left(x \right)}}{\left(1 - e^{x}\right)^{\frac{3}{2}}} + 4 \sqrt{1 - e^{x}} \left(x \cos{\left(x \right)} + 2 \sin{\left(x \right)}\right) - \frac{2 \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right) e^{x}}{\sqrt{1 - e^{x}}} + \frac{2 e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}}\right)}{x \left(e^{x} - 1\right) \cos{\left(x \right)}} + \frac{32 \left(\frac{x e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}} + 2 \sqrt{1 - e^{x}} \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right)\right) \sin{\left(x \right)}}{x \sqrt{1 - e^{x}} \cos{\left(x \right)}} + \frac{16 \left(- \frac{2 x e^{x} \sin{\left(x \right)}}{\sqrt{1 - e^{x}}} + \frac{2 x e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}} + \frac{x e^{2 x} \cos{\left(x \right)}}{\left(1 - e^{x}\right)^{\frac{3}{2}}} + 4 \sqrt{1 - e^{x}} \left(x \cos{\left(x \right)} + 2 \sin{\left(x \right)}\right) - \frac{2 \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right) e^{x}}{\sqrt{1 - e^{x}}} + \frac{2 e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}}\right)}{x \sqrt{1 - e^{x}}} + \frac{16 \left(\frac{x e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}} + 2 \sqrt{1 - e^{x}} \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right)\right) e^{x}}{x \left(1 - e^{x}\right)^{\frac{3}{2}}} + \frac{12 \left(\frac{x e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}} + 2 \sqrt{1 - e^{x}} \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right)\right) \left(2 x \sqrt{1 - e^{x}} \sin{\left(x \right)} + \frac{x e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}} - 2 \sqrt{1 - e^{x}} \cos{\left(x \right)}\right)}{x^{2} \left(e^{x} - 1\right) \cos{\left(x \right)}} - \frac{32 \left(\frac{x e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}} + 2 \sqrt{1 - e^{x}} \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right)\right)}{x^{2} \sqrt{1 - e^{x}}} - \frac{\left(\frac{x e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}} + 2 \sqrt{1 - e^{x}} \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right)\right) \left(2 x \sqrt{1 - e^{x}} \sin{\left(x \right)} + \frac{x e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}} - 2 \sqrt{1 - e^{x}} \cos{\left(x \right)}\right)^{2}}{x^{2} \left(1 - e^{x}\right)^{\frac{3}{2}} \cos^{2}{\left(x \right)}}\right)}{64 x \cos{\left(x \right)}}$$
Gráfico