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 (π-2x)³
-
Derivada de y=e×
-
Derivada de y/(sqrt(5^2+y^2))
-
Derivada de y=(3x-7)4
-
Expresiones idénticas
- (x*sin(x)*(uno -e^x)^(uno / dos))^(uno / dos)
- (x multiplicar por seno de (x) multiplicar por (1 menos e en el grado x) en el grado (1 dividir por 2)) en el grado (1 dividir por 2)
- (x multiplicar por seno de (x) multiplicar por (uno menos e en el grado x) en el grado (uno dividir por dos)) en el grado (uno dividir por dos)
- (x*sin(x)*(1-ex)(1/2))(1/2)
- x*sinx*1-ex1/21/2
- (xsin(x)(1-e^x)^(1/2))^(1/2)
- (xsin(x)(1-ex)(1/2))(1/2)
- xsinx1-ex1/21/2
- xsinx1-e^x^1/2^1/2
- (x*sin(x)*(1-e^x)^(1 dividir por 2))^(1 dividir por 2)
-
Expresiones semejantes
- (x*sin(x)*(1+e^x)^(1/2))^(1/2)
- (x*sinx*(1-e^x)^(1/2))^(1/2)
Derivada de (x*sin(x)*(1-e^x)^(1/2))^(1/2)
Solución
Ha introducido
[src]
______________________ / ________ / / x \/ x*sin(x)*\/ 1 - E
$$\sqrt{x \sin{\left(x \right)} \sqrt{1 - e^{x}}}$$
sqrt((x*sin(x))*sqrt(1 - E^x))
Solución detallada
-
Sustituimos .
-
Según el principio, aplicamos: tenemos
-
Luego se aplica una cadena de reglas. Multiplicamos por :
-
Se aplica la regla de la derivada de una multiplicación:
; calculamos :
-
Se aplica la regla de la derivada de una multiplicación:
; calculamos :
-
Según el principio, aplicamos: tenemos
; calculamos :
-
La derivada del seno es igual al coseno:
Como resultado de:
-
; calculamos :
-
Sustituimos .
-
Según el principio, aplicamos: tenemos
-
-
Luego se aplica una cadena de reglas. Multiplicamos por :
-
diferenciamos miembro por miembro:
-
La derivada de una constante es igual a cero.
-
La derivada del producto de una constante por función es igual al producto de esta constante por la derivada de esta función.
-
Derivado es.
Entonces, como resultado:
-
Como resultado de:
-
Como resultado de la secuencia de reglas:
-
Como resultado de:
-
Como resultado de la secuencia de reglas:
Simplificamos:
Respuesta:
Primera derivada
[src]
______________________ / ________ \
/ ________ | / x x |
/ / x |\/ 1 - E *(x*cos(x) + sin(x)) x*e *sin(x) |
\/ x*\/ 1 - E *sin(x) *|------------------------------- - -------------|
| 2 ________|
| / x |
\ 4*\/ 1 - E /
----------------------------------------------------------------------------
________
/ x
x*\/ 1 - E *sin(x)
$$\frac{\sqrt{x \sqrt{1 - e^{x}} \sin{\left(x \right)}} \left(- \frac{x e^{x} \sin{\left(x \right)}}{4 \sqrt{1 - e^{x}}} + \frac{\sqrt{1 - e^{x}} \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)}{2}\right)}{x \sqrt{1 - e^{x}} \sin{\left(x \right)}}$$
Segunda derivada
[src]
/ / ________ x x 2*x x x \ / ________ x \ / ________ x \ / ________ x \ / ________ x \ / ________ ________ x \\
| | / x 2*(x*cos(x) + sin(x))*e 2*e *sin(x) x*e *sin(x) 2*x*cos(x)*e 2*x*e *sin(x)| | / x x*e *sin(x)| x | / x x*e *sin(x)| | / x x*e *sin(x)| | / x x*e *sin(x)| | / x / x x*e *sin(x)||
| 2*|4*\/ 1 - e *(-2*cos(x) + x*sin(x)) + ------------------------ + ----------- + ------------- + ------------- + -------------| 2*|- 2*\/ 1 - e *(x*cos(x) + sin(x)) + -----------|*e 4*|- 2*\/ 1 - e *(x*cos(x) + sin(x)) + -----------| 4*|- 2*\/ 1 - e *(x*cos(x) + sin(x)) + -----------|*cos(x) |- 2*\/ 1 - e *(x*cos(x) + sin(x)) + -----------|*|2*\/ 1 - e *sin(x) + 2*x*\/ 1 - e *cos(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 *sin(x) *|- --------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------- + ----------------------------------------------------- + ------------------------------------------------------------ + -----------------------------------------------------------------------------------------------------------------|
| ________ 3/2 ________ ________ / x\ |
| / x / x\ / x / x x*\-1 + e /*sin(x) |
\ \/ 1 - e \1 - e / x*\/ 1 - e \/ 1 - e *sin(x) /
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
16*x*sin(x)
$$\frac{\sqrt{x \sqrt{1 - e^{x}} \sin{\left(x \right)}} \left(\frac{4 \left(\frac{x e^{x} \sin{\left(x \right)}}{\sqrt{1 - e^{x}}} - 2 \sqrt{1 - e^{x}} \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)\right) \cos{\left(x \right)}}{\sqrt{1 - e^{x}} \sin{\left(x \right)}} - \frac{2 \left(\frac{2 x e^{x} \sin{\left(x \right)}}{\sqrt{1 - e^{x}}} + \frac{2 x e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}} + \frac{x e^{2 x} \sin{\left(x \right)}}{\left(1 - e^{x}\right)^{\frac{3}{2}}} + 4 \sqrt{1 - e^{x}} \left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) + \frac{2 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) e^{x}}{\sqrt{1 - e^{x}}} + \frac{2 e^{x} \sin{\left(x \right)}}{\sqrt{1 - e^{x}}}\right)}{\sqrt{1 - e^{x}}} - \frac{2 \left(\frac{x e^{x} \sin{\left(x \right)}}{\sqrt{1 - e^{x}}} - 2 \sqrt{1 - e^{x}} \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)\right) e^{x}}{\left(1 - e^{x}\right)^{\frac{3}{2}}} + \frac{\left(\frac{x e^{x} \sin{\left(x \right)}}{\sqrt{1 - e^{x}}} - 2 \sqrt{1 - e^{x}} \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)\right) \left(2 x \sqrt{1 - e^{x}} \cos{\left(x \right)} - \frac{x e^{x} \sin{\left(x \right)}}{\sqrt{1 - e^{x}}} + 2 \sqrt{1 - e^{x}} \sin{\left(x \right)}\right)}{x \left(e^{x} - 1\right) \sin{\left(x \right)}} + \frac{4 \left(\frac{x e^{x} \sin{\left(x \right)}}{\sqrt{1 - e^{x}}} - 2 \sqrt{1 - e^{x}} \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)\right)}{x \sqrt{1 - e^{x}}}\right)}{16 x \sin{\left(x \right)}}$$
Tercera derivada
[src]
/ 2 \
| / ________ x \ / ________ x 2*x 2*x x x x 3*x 2*x 2*x x\ / ________ x \ / ________ x \ / ________ x \ / ________ x x 2*x x x \ / ________ x x 2*x x x \ / ________ x \ / ________ x \ / ________ x x 2*x x x \ / ________ ________ x \ / ________ x \ / ________ x \ / ________ x \ / ________ ________ x \ / ________ x \ / ________ ________ x 2*x x x\ / ________ ________ x \ / ________ x x 2*x x x \ / ________ x \ / ________ x \ / ________ ________ x \ / ________ x \ / ________ ________ x \ |
| | / x x*e *sin(x)| | / x 8*(-2*cos(x) + x*sin(x))*e 2*(x*cos(x) + sin(x))*e 4*e *sin(x) 4*(x*cos(x) + sin(x))*e 8*cos(x)*e 8*e *sin(x) 3*x*e *sin(x) 4*x*cos(x)*e 6*x*e *sin(x) 8*x*cos(x)*e | | / x x*e *sin(x)| | / x x*e *sin(x)| 2*x | / x x*e *sin(x)| x | / x 2*(x*cos(x) + sin(x))*e 2*e *sin(x) x*e *sin(x) 2*x*cos(x)*e 2*x*e *sin(x)| x | / x 2*(x*cos(x) + sin(x))*e 2*e *sin(x) x*e *sin(x) 2*x*cos(x)*e 2*x*e *sin(x)| 2 | / x x*e *sin(x)| | / x x*e *sin(x)| x | / x 2*(x*cos(x) + sin(x))*e 2*e *sin(x) x*e *sin(x) 2*x*cos(x)*e 2*x*e *sin(x)| | / x / x x*e *sin(x)| | / x x*e *sin(x)| | / x x*e *sin(x)| | / x x*e *sin(x)| | / x / x x*e *sin(x)| | / x x*e *sin(x)| | / x / x 4*e *sin(x) x*e *sin(x) 2*x*e *sin(x) 4*x*cos(x)*e | | / x / x x*e *sin(x)| | / x 2*(x*cos(x) + sin(x))*e 2*e *sin(x) x*e *sin(x) 2*x*cos(x)*e 2*x*e *sin(x)| | / x x*e *sin(x)| x | / x x*e *sin(x)| | / x / x x*e *sin(x)| | / x x*e *sin(x)| | / x / x x*e *sin(x)| x|
| 16*|- 2*\/ 1 - e *(x*cos(x) + sin(x)) + -----------| 4*|8*\/ 1 - e *(3*sin(x) + x*cos(x)) - --------------------------- + -------------------------- + ------------- + ------------------------ + ----------- + ----------- + --------------- + --------------- + --------------- + -------------| 32*|- 2*\/ 1 - e *(x*cos(x) + sin(x)) + -----------| 12*|- 2*\/ 1 - e *(x*cos(x) + sin(x)) + -----------|*e 8*|- 2*\/ 1 - e *(x*cos(x) + sin(x)) + -----------|*e 8*|4*\/ 1 - e *(-2*cos(x) + x*sin(x)) + ------------------------ + ----------- + ------------- + ------------- + -------------|*e 16*|4*\/ 1 - e *(-2*cos(x) + x*sin(x)) + ------------------------ + ----------- + ------------- + ------------- + -------------| 32*cos (x)*|- 2*\/ 1 - e *(x*cos(x) + sin(x)) + -----------| 16*|- 2*\/ 1 - e *(x*cos(x) + sin(x)) + -----------|*e 16*|4*\/ 1 - e *(-2*cos(x) + x*sin(x)) + ------------------------ + ----------- + ------------- + ------------- + -------------|*cos(x) |2*\/ 1 - e *sin(x) + 2*x*\/ 1 - e *cos(x) - -----------| *|- 2*\/ 1 - e *(x*cos(x) + sin(x)) + -----------| 32*|- 2*\/ 1 - e *(x*cos(x) + sin(x)) + -----------|*cos(x) 12*|- 2*\/ 1 - e *(x*cos(x) + sin(x)) + -----------|*|2*\/ 1 - e *sin(x) + 2*x*\/ 1 - e *cos(x) - -----------| 2*|- 2*\/ 1 - e *(x*cos(x) + sin(x)) + -----------|*|- 8*\/ 1 - e *cos(x) + 4*x*\/ 1 - e *sin(x) + ----------- + ------------- + ------------- + -------------| 4*|2*\/ 1 - e *sin(x) + 2*x*\/ 1 - e *cos(x) - -----------|*|4*\/ 1 - e *(-2*cos(x) + x*sin(x)) + ------------------------ + ----------- + ------------- + ------------- + -------------| 16*|- 2*\/ 1 - e *(x*cos(x) + sin(x)) + -----------|*cos(x)*e 12*|- 2*\/ 1 - e *(x*cos(x) + sin(x)) + -----------|*|2*\/ 1 - e *sin(x) + 2*x*\/ 1 - e *cos(x) - -----------|*cos(x) 6*|- 2*\/ 1 - e *(x*cos(x) + sin(x)) + -----------|*|2*\/ 1 - e *sin(x) + 2*x*\/ 1 - e *cos(x) - -----------|*e |
______________________ | | ________| | ________ 3/2 3/2 ________ ________ ________ 5/2 3/2 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 *sin(x) *|- ------------------------------------------------------ - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------ - ----------------------------------------------------------- - -------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------ + ---------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------- + --------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------|
| ________ ________ ________ 5/2 3/2 3/2 ________ ________ 3/2 ________ 3/2 ________ 2 / x\ / x\ / x\ 3/2 / x\ 2 2 |
| / x / x 2 / x / x\ / x\ / x\ / x / x 2 / x\ / x 2 / x\ 2 / x x *\-1 + e /*sin(x) x*\-1 + e /*sin(x) x*\-1 + e /*sin(x) / x\ x*\-1 + e /*sin (x) / x\ |
\ \/ 1 - e \/ 1 - e x *\/ 1 - e \1 - e / \1 - e / \1 - e / x*\/ 1 - e \/ 1 - e *sin (x) x*\1 - e / \/ 1 - e *sin(x) x *\1 - e / *sin (x) x*\/ 1 - e *sin(x) \1 - e / *sin(x) x*\-1 + e / *sin(x) /
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
64*x*sin(x)
$$\frac{\sqrt{x \sqrt{1 - e^{x}} \sin{\left(x \right)}} \left(- \frac{16 \left(\frac{x e^{x} \sin{\left(x \right)}}{\sqrt{1 - e^{x}}} - 2 \sqrt{1 - e^{x}} \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)\right)}{\sqrt{1 - e^{x}}} - \frac{32 \left(\frac{x e^{x} \sin{\left(x \right)}}{\sqrt{1 - e^{x}}} - 2 \sqrt{1 - e^{x}} \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)\right) \cos^{2}{\left(x \right)}}{\sqrt{1 - e^{x}} \sin^{2}{\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} \sin{\left(x \right)}}{\left(1 - e^{x}\right)^{\frac{3}{2}}} + 4 \sqrt{1 - e^{x}} \left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) + \frac{2 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) e^{x}}{\sqrt{1 - e^{x}}} + \frac{2 e^{x} \sin{\left(x \right)}}{\sqrt{1 - e^{x}}}\right) \cos{\left(x \right)}}{\sqrt{1 - e^{x}} \sin{\left(x \right)}} - \frac{4 \left(\frac{8 x e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}} + \frac{6 x e^{2 x} \sin{\left(x \right)}}{\left(1 - e^{x}\right)^{\frac{3}{2}}} + \frac{4 x e^{2 x} \cos{\left(x \right)}}{\left(1 - e^{x}\right)^{\frac{3}{2}}} + \frac{3 x e^{3 x} \sin{\left(x \right)}}{\left(1 - e^{x}\right)^{\frac{5}{2}}} + 8 \sqrt{1 - e^{x}} \left(x \cos{\left(x \right)} + 3 \sin{\left(x \right)}\right) - \frac{8 \left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) e^{x}}{\sqrt{1 - e^{x}}} + \frac{4 \left(x \cos{\left(x \right)} + \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 \cos{\left(x \right)} + \sin{\left(x \right)}\right) e^{2 x}}{\left(1 - e^{x}\right)^{\frac{3}{2}}} + \frac{4 e^{2 x} \sin{\left(x \right)}}{\left(1 - e^{x}\right)^{\frac{3}{2}}}\right)}{\sqrt{1 - e^{x}}} - \frac{8 \left(\frac{x e^{x} \sin{\left(x \right)}}{\sqrt{1 - e^{x}}} - 2 \sqrt{1 - e^{x}} \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)\right) e^{x}}{\left(1 - e^{x}\right)^{\frac{3}{2}}} + \frac{16 \left(\frac{x e^{x} \sin{\left(x \right)}}{\sqrt{1 - e^{x}}} - 2 \sqrt{1 - e^{x}} \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)\right) e^{x} \cos{\left(x \right)}}{\left(1 - e^{x}\right)^{\frac{3}{2}} \sin{\left(x \right)}} - \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} \sin{\left(x \right)}}{\left(1 - e^{x}\right)^{\frac{3}{2}}} + 4 \sqrt{1 - e^{x}} \left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) + \frac{2 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) e^{x}}{\sqrt{1 - e^{x}}} + \frac{2 e^{x} \sin{\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} \sin{\left(x \right)}}{\sqrt{1 - e^{x}}} - 2 \sqrt{1 - e^{x}} \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)\right) e^{2 x}}{\left(1 - e^{x}\right)^{\frac{5}{2}}} - \frac{12 \left(\frac{x e^{x} \sin{\left(x \right)}}{\sqrt{1 - e^{x}}} - 2 \sqrt{1 - e^{x}} \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)\right) \left(2 x \sqrt{1 - e^{x}} \cos{\left(x \right)} - \frac{x e^{x} \sin{\left(x \right)}}{\sqrt{1 - e^{x}}} + 2 \sqrt{1 - e^{x}} \sin{\left(x \right)}\right) \cos{\left(x \right)}}{x \left(e^{x} - 1\right) \sin^{2}{\left(x \right)}} - \frac{2 \left(\frac{x e^{x} \sin{\left(x \right)}}{\sqrt{1 - e^{x}}} - 2 \sqrt{1 - e^{x}} \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)\right) \left(4 x \sqrt{1 - e^{x}} \sin{\left(x \right)} + \frac{2 x e^{x} \sin{\left(x \right)}}{\sqrt{1 - e^{x}}} + \frac{4 x e^{x} \cos{\left(x \right)}}{\sqrt{1 - e^{x}}} + \frac{x e^{2 x} \sin{\left(x \right)}}{\left(1 - e^{x}\right)^{\frac{3}{2}}} - 8 \sqrt{1 - e^{x}} \cos{\left(x \right)} + \frac{4 e^{x} \sin{\left(x \right)}}{\sqrt{1 - e^{x}}}\right)}{x \left(e^{x} - 1\right) \sin{\left(x \right)}} - \frac{6 \left(\frac{x e^{x} \sin{\left(x \right)}}{\sqrt{1 - e^{x}}} - 2 \sqrt{1 - e^{x}} \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)\right) \left(2 x \sqrt{1 - e^{x}} \cos{\left(x \right)} - \frac{x e^{x} \sin{\left(x \right)}}{\sqrt{1 - e^{x}}} + 2 \sqrt{1 - e^{x}} \sin{\left(x \right)}\right) e^{x}}{x \left(e^{x} - 1\right)^{2} \sin{\left(x \right)}} + \frac{4 \left(2 x \sqrt{1 - e^{x}} \cos{\left(x \right)} - \frac{x e^{x} \sin{\left(x \right)}}{\sqrt{1 - e^{x}}} + 2 \sqrt{1 - e^{x}} \sin{\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} \sin{\left(x \right)}}{\left(1 - e^{x}\right)^{\frac{3}{2}}} + 4 \sqrt{1 - e^{x}} \left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) + \frac{2 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) e^{x}}{\sqrt{1 - e^{x}}} + \frac{2 e^{x} \sin{\left(x \right)}}{\sqrt{1 - e^{x}}}\right)}{x \left(e^{x} - 1\right) \sin{\left(x \right)}} - \frac{32 \left(\frac{x e^{x} \sin{\left(x \right)}}{\sqrt{1 - e^{x}}} - 2 \sqrt{1 - e^{x}} \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)\right) \cos{\left(x \right)}}{x \sqrt{1 - e^{x}} \sin{\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} \sin{\left(x \right)}}{\left(1 - e^{x}\right)^{\frac{3}{2}}} + 4 \sqrt{1 - e^{x}} \left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) + \frac{2 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) e^{x}}{\sqrt{1 - e^{x}}} + \frac{2 e^{x} \sin{\left(x \right)}}{\sqrt{1 - e^{x}}}\right)}{x \sqrt{1 - e^{x}}} + \frac{16 \left(\frac{x e^{x} \sin{\left(x \right)}}{\sqrt{1 - e^{x}}} - 2 \sqrt{1 - e^{x}} \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)\right) e^{x}}{x \left(1 - e^{x}\right)^{\frac{3}{2}}} - \frac{12 \left(\frac{x e^{x} \sin{\left(x \right)}}{\sqrt{1 - e^{x}}} - 2 \sqrt{1 - e^{x}} \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)\right) \left(2 x \sqrt{1 - e^{x}} \cos{\left(x \right)} - \frac{x e^{x} \sin{\left(x \right)}}{\sqrt{1 - e^{x}}} + 2 \sqrt{1 - e^{x}} \sin{\left(x \right)}\right)}{x^{2} \left(e^{x} - 1\right) \sin{\left(x \right)}} - \frac{32 \left(\frac{x e^{x} \sin{\left(x \right)}}{\sqrt{1 - e^{x}}} - 2 \sqrt{1 - e^{x}} \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)\right)}{x^{2} \sqrt{1 - e^{x}}} - \frac{\left(\frac{x e^{x} \sin{\left(x \right)}}{\sqrt{1 - e^{x}}} - 2 \sqrt{1 - e^{x}} \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)\right) \left(2 x \sqrt{1 - e^{x}} \cos{\left(x \right)} - \frac{x e^{x} \sin{\left(x \right)}}{\sqrt{1 - e^{x}}} + 2 \sqrt{1 - e^{x}} \sin{\left(x \right)}\right)^{2}}{x^{2} \left(1 - e^{x}\right)^{\frac{3}{2}} \sin^{2}{\left(x \right)}}\right)}{64 x \sin{\left(x \right)}}$$
Gráfico