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^((3*x)^2)
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Derivada de d/dx(x)
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Derivada de (cos(x))^x^2
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Derivada de (8*x-15)^5
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Expresiones idénticas
- x*exp(-x)exp^(((x^(dos)+x)*sin(x))^(uno / dos))
- x multiplicar por exponente de ( menos x) exponente de en el grado (((x en el grado (2) más x) multiplicar por seno de (x)) en el grado (1 dividir por 2))
- x multiplicar por exponente de ( menos x) exponente de en el grado (((x en el grado (dos) más x) multiplicar por seno de (x)) en el grado (uno dividir por dos))
- x*exp(-x)exp(((x(2)+x)*sin(x))(1/2))
- x*exp-xexpx2+x*sinx1/2
- xexp(-x)exp^(((x^(2)+x)sin(x))^(1/2))
- xexp(-x)exp(((x(2)+x)sin(x))(1/2))
- xexp-xexpx2+xsinx1/2
- xexp-xexp^x^2+xsinx^1/2
- x*exp(-x)exp^(((x^(2)+x)*sin(x))^(1 dividir por 2))
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Expresiones semejantes
- x*exp(x)exp^(((x^(2)+x)*sin(x))^(1/2))
- x*exp(-x)exp^(((x^(2)-x)*sin(x))^(1/2))
- x*exp(-x)exp^(((x^(2)+x)*sinx)^(1/2))
Derivada de x*exp(-x)exp^(((x^(2)+x)*sin(x))^(1/2))
Solución
Ha introducido
[src]
_________________
/ / 2 \
-x \/ \x + x/*sin(x)
x*e *E
$$e^{\sqrt{\left(x^{2} + x\right) \sin{\left(x \right)}}} x e^{- x}$$
(x*exp(-x))*E^(sqrt((x^2 + x)*sin(x)))
Solución detallada
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Se aplica la regla de la derivada parcial:
y .
Para calcular :
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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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Sustituimos .
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Derivado es.
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Luego se aplica una cadena de reglas. Multiplicamos por :
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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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diferenciamos miembro por miembro:
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Según el principio, aplicamos: tenemos
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Según el principio, aplicamos: tenemos
Como resultado de:
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; calculamos :
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La derivada del seno es igual al coseno:
Como resultado de:
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Como resultado de la secuencia de reglas:
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Como resultado de la secuencia de reglas:
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Como resultado de:
Para calcular :
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Derivado es.
Ahora aplicamos la regla de la derivada de una divesión:
Simplificamos:
Respuesta:
Primera derivada
[src]
_________________
_________________ / / 2 \ \ / / 2 \
_________________ / / 2 \ |(1 + 2*x)*sin(x) \x + x/*cos(x)| \/ \x + x/*sin(x) -x
/ / 2 \ x*\/ \x + x/*sin(x) *|---------------- + ---------------|*e *e
/ -x -x\ \/ \x + x/*sin(x) \ 2 2 /
\- x*e + e /*e + -------------------------------------------------------------------------------------
/ 2 \
\x + x/*sin(x)
$$\frac{x \sqrt{\left(x^{2} + x\right) \sin{\left(x \right)}} \left(\frac{\left(2 x + 1\right) \sin{\left(x \right)}}{2} + \frac{\left(x^{2} + x\right) \cos{\left(x \right)}}{2}\right) e^{- x} e^{\sqrt{\left(x^{2} + x\right) \sin{\left(x \right)}}}}{\left(x^{2} + x\right) \sin{\left(x \right)}} + \left(- x e^{- x} + e^{- x}\right) e^{\sqrt{\left(x^{2} + x\right) \sin{\left(x \right)}}}$$
Segunda derivada
[src]
/ __________________ __________________ 2 __________________ \ | 2 __________________ 2*\/ x*(1 + x)*sin(x) *((1 + 2*x)*sin(x) + x*(1 + x)*cos(x))*cos(x) \/ x*(1 + x)*sin(x) *((1 + 2*x)*sin(x) + x*(1 + x)*cos(x)) 2*\/ x*(1 + x)*sin(x) *(1 + 2*x)*((1 + 2*x)*sin(x) + x*(1 + x)*cos(x)) | | ((1 + 2*x)*sin(x) + x*(1 + x)*cos(x)) + 2*\/ x*(1 + x)*sin(x) *(2*sin(x) + 2*(1 + 2*x)*cos(x) - x*(1 + x)*sin(x)) - ------------------------------------------------------------------- + ----------------------------------------------------------- - ---------------------------------------------------------------------- __________________ | __________________ | sin(x) x*(1 + x)*sin(x) x*(1 + x) \/ x*(1 + x)*sin(x) *(-1 + x)*((1 + 2*x)*sin(x) + x*(1 + x)*cos(x))| \/ x*(1 + x)*sin(x) -x |-2 + x + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------|*e *e \ 4*(1 + x)*sin(x) x*(1 + x)*sin(x) /
$$\left(x - 2 + \frac{- \frac{2 \sqrt{x \left(x + 1\right) \sin{\left(x \right)}} \left(x \left(x + 1\right) \cos{\left(x \right)} + \left(2 x + 1\right) \sin{\left(x \right)}\right) \cos{\left(x \right)}}{\sin{\left(x \right)}} + 2 \sqrt{x \left(x + 1\right) \sin{\left(x \right)}} \left(- x \left(x + 1\right) \sin{\left(x \right)} + 2 \left(2 x + 1\right) \cos{\left(x \right)} + 2 \sin{\left(x \right)}\right) + \left(x \left(x + 1\right) \cos{\left(x \right)} + \left(2 x + 1\right) \sin{\left(x \right)}\right)^{2} - \frac{2 \sqrt{x \left(x + 1\right) \sin{\left(x \right)}} \left(2 x + 1\right) \left(x \left(x + 1\right) \cos{\left(x \right)} + \left(2 x + 1\right) \sin{\left(x \right)}\right)}{x \left(x + 1\right)} + \frac{\sqrt{x \left(x + 1\right) \sin{\left(x \right)}} \left(x \left(x + 1\right) \cos{\left(x \right)} + \left(2 x + 1\right) \sin{\left(x \right)}\right)^{2}}{x \left(x + 1\right) \sin{\left(x \right)}}}{4 \left(x + 1\right) \sin{\left(x \right)}} - \frac{\sqrt{x \left(x + 1\right) \sin{\left(x \right)}} \left(x - 1\right) \left(x \left(x + 1\right) \cos{\left(x \right)} + \left(2 x + 1\right) \sin{\left(x \right)}\right)}{x \left(x + 1\right) \sin{\left(x \right)}}\right) e^{- x} e^{\sqrt{x \left(x + 1\right) \sin{\left(x \right)}}}$$
Tercera derivada
[src]
/ 2 __________________ __________________ 2 3 __________________ 2 __________________ 3 __________________ 3 __________________ __________________ 2 __________________ 2 __________________ 2 __________________ __________________ \ | __________________ __________________ 6*((1 + 2*x)*sin(x) + x*(1 + x)*cos(x)) *cos(x) 8*\/ x*(1 + x)*sin(x) *((1 + 2*x)*sin(x) + x*(1 + x)*cos(x)) 8*\/ x*(1 + x)*sin(x) *(2*sin(x) + 2*(1 + 2*x)*cos(x) - x*(1 + x)*sin(x))*cos(x) 6*((1 + 2*x)*sin(x) + x*(1 + x)*cos(x)) *(1 + 2*x) 3*((1 + 2*x)*sin(x) + x*(1 + x)*cos(x)) 8*\/ x*(1 + x)*sin(x) *cos (x)*((1 + 2*x)*sin(x) + x*(1 + x)*cos(x)) \/ x*(1 + x)*sin(x) *((1 + 2*x)*sin(x) + x*(1 + x)*cos(x)) \/ x*(1 + x)*sin(x) *((1 + 2*x)*sin(x) + x*(1 + x)*cos(x)) 8*\/ x*(1 + x)*sin(x) *(1 + 2*x)*(2*sin(x) + 2*(1 + 2*x)*cos(x) - x*(1 + x)*sin(x)) 8*\/ x*(1 + x)*sin(x) *(1 + 2*x) *((1 + 2*x)*sin(x) + x*(1 + x)*cos(x)) 6*\/ x*(1 + x)*sin(x) *((1 + 2*x)*sin(x) + x*(1 + x)*cos(x)) *cos(x) 6*\/ x*(1 + x)*sin(x) *((1 + 2*x)*sin(x) + x*(1 + x)*cos(x)) *(1 + 2*x) 6*\/ x*(1 + x)*sin(x) *((1 + 2*x)*sin(x) + x*(1 + x)*cos(x))*(2*sin(x) + 2*(1 + 2*x)*cos(x) - x*(1 + x)*sin(x)) 8*\/ x*(1 + x)*sin(x) *(1 + 2*x)*((1 + 2*x)*sin(x) + x*(1 + x)*cos(x))*cos(x) / __________________ __________________ 2 __________________ \ | | - 4*\/ x*(1 + x)*sin(x) *(-6*cos(x) + 3*(1 + 2*x)*sin(x) + x*(1 + x)*cos(x)) + 4*\/ x*(1 + x)*sin(x) *((1 + 2*x)*sin(x) + x*(1 + x)*cos(x)) + 6*((1 + 2*x)*sin(x) + x*(1 + x)*cos(x))*(2*sin(x) + 2*(1 + 2*x)*cos(x) - x*(1 + x)*sin(x)) - ----------------------------------------------- - ------------------------------------------------------------ - -------------------------------------------------------------------------------- - -------------------------------------------------- + ---------------------------------------- + -------------------------------------------------------------------- + ----------------------------------------------------------- + ----------------------------------------------------------- - ----------------------------------------------------------------------------------- + ----------------------------------------------------------------------- - -------------------------------------------------------------------- - ----------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------- | 2 __________________ 2*\/ x*(1 + x)*sin(x) *((1 + 2*x)*sin(x) + x*(1 + x)*cos(x))*cos(x) \/ x*(1 + x)*sin(x) *((1 + 2*x)*sin(x) + x*(1 + x)*cos(x)) 2*\/ x*(1 + x)*sin(x) *(1 + 2*x)*((1 + 2*x)*sin(x) + x*(1 + x)*cos(x))| | | sin(x) x*(1 + x) sin(x) x*(1 + x) x*(1 + x)*sin(x) 2 x*(1 + x)*sin(x) 2 2 2 x*(1 + x) 2 2 2 2 2 x*(1 + x)*sin(x) x*(1 + x)*sin(x) 3*(-1 + x)*|((1 + 2*x)*sin(x) + x*(1 + x)*cos(x)) + 2*\/ x*(1 + x)*sin(x) *(2*sin(x) + 2*(1 + 2*x)*cos(x) - x*(1 + x)*sin(x)) - ------------------------------------------------------------------- + ----------------------------------------------------------- - ----------------------------------------------------------------------| __________________ | __________________ | sin (x) x *(1 + x) *sin (x) x *(1 + x) x*(1 + x)*sin (x) x *(1 + x) *sin(x) \ sin(x) x*(1 + x)*sin(x) x*(1 + x) / 3*\/ x*(1 + x)*sin(x) *(-2 + x)*((1 + 2*x)*sin(x) + x*(1 + x)*cos(x))| \/ x*(1 + x)*sin(x) -x |3 - x + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------|*e *e \ 8*(1 + x)*sin(x) 4*x*(1 + x)*sin(x) 2*x*(1 + x)*sin(x) /
$$\left(- x + 3 + \frac{4 \sqrt{x \left(x + 1\right) \sin{\left(x \right)}} \left(x \left(x + 1\right) \cos{\left(x \right)} + \left(2 x + 1\right) \sin{\left(x \right)}\right) + \frac{8 \sqrt{x \left(x + 1\right) \sin{\left(x \right)}} \left(x \left(x + 1\right) \cos{\left(x \right)} + \left(2 x + 1\right) \sin{\left(x \right)}\right) \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} - \frac{8 \sqrt{x \left(x + 1\right) \sin{\left(x \right)}} \left(- x \left(x + 1\right) \sin{\left(x \right)} + 2 \left(2 x + 1\right) \cos{\left(x \right)} + 2 \sin{\left(x \right)}\right) \cos{\left(x \right)}}{\sin{\left(x \right)}} - 4 \sqrt{x \left(x + 1\right) \sin{\left(x \right)}} \left(x \left(x + 1\right) \cos{\left(x \right)} + 3 \left(2 x + 1\right) \sin{\left(x \right)} - 6 \cos{\left(x \right)}\right) - \frac{6 \left(x \left(x + 1\right) \cos{\left(x \right)} + \left(2 x + 1\right) \sin{\left(x \right)}\right)^{2} \cos{\left(x \right)}}{\sin{\left(x \right)}} + 6 \left(x \left(x + 1\right) \cos{\left(x \right)} + \left(2 x + 1\right) \sin{\left(x \right)}\right) \left(- x \left(x + 1\right) \sin{\left(x \right)} + 2 \left(2 x + 1\right) \cos{\left(x \right)} + 2 \sin{\left(x \right)}\right) + \frac{8 \sqrt{x \left(x + 1\right) \sin{\left(x \right)}} \left(2 x + 1\right) \left(x \left(x + 1\right) \cos{\left(x \right)} + \left(2 x + 1\right) \sin{\left(x \right)}\right) \cos{\left(x \right)}}{x \left(x + 1\right) \sin{\left(x \right)}} - \frac{8 \sqrt{x \left(x + 1\right) \sin{\left(x \right)}} \left(2 x + 1\right) \left(- x \left(x + 1\right) \sin{\left(x \right)} + 2 \left(2 x + 1\right) \cos{\left(x \right)} + 2 \sin{\left(x \right)}\right)}{x \left(x + 1\right)} + \frac{\sqrt{x \left(x + 1\right) \sin{\left(x \right)}} \left(x \left(x + 1\right) \cos{\left(x \right)} + \left(2 x + 1\right) \sin{\left(x \right)}\right)^{3}}{x \left(x + 1\right) \sin{\left(x \right)}} - \frac{6 \sqrt{x \left(x + 1\right) \sin{\left(x \right)}} \left(x \left(x + 1\right) \cos{\left(x \right)} + \left(2 x + 1\right) \sin{\left(x \right)}\right)^{2} \cos{\left(x \right)}}{x \left(x + 1\right) \sin^{2}{\left(x \right)}} + \frac{6 \sqrt{x \left(x + 1\right) \sin{\left(x \right)}} \left(x \left(x + 1\right) \cos{\left(x \right)} + \left(2 x + 1\right) \sin{\left(x \right)}\right) \left(- x \left(x + 1\right) \sin{\left(x \right)} + 2 \left(2 x + 1\right) \cos{\left(x \right)} + 2 \sin{\left(x \right)}\right)}{x \left(x + 1\right) \sin{\left(x \right)}} - \frac{8 \sqrt{x \left(x + 1\right) \sin{\left(x \right)}} \left(x \left(x + 1\right) \cos{\left(x \right)} + \left(2 x + 1\right) \sin{\left(x \right)}\right)}{x \left(x + 1\right)} - \frac{6 \left(2 x + 1\right) \left(x \left(x + 1\right) \cos{\left(x \right)} + \left(2 x + 1\right) \sin{\left(x \right)}\right)^{2}}{x \left(x + 1\right)} + \frac{3 \left(x \left(x + 1\right) \cos{\left(x \right)} + \left(2 x + 1\right) \sin{\left(x \right)}\right)^{3}}{x \left(x + 1\right) \sin{\left(x \right)}} + \frac{8 \sqrt{x \left(x + 1\right) \sin{\left(x \right)}} \left(2 x + 1\right)^{2} \left(x \left(x + 1\right) \cos{\left(x \right)} + \left(2 x + 1\right) \sin{\left(x \right)}\right)}{x^{2} \left(x + 1\right)^{2}} - \frac{6 \sqrt{x \left(x + 1\right) \sin{\left(x \right)}} \left(2 x + 1\right) \left(x \left(x + 1\right) \cos{\left(x \right)} + \left(2 x + 1\right) \sin{\left(x \right)}\right)^{2}}{x^{2} \left(x + 1\right)^{2} \sin{\left(x \right)}} + \frac{\sqrt{x \left(x + 1\right) \sin{\left(x \right)}} \left(x \left(x + 1\right) \cos{\left(x \right)} + \left(2 x + 1\right) \sin{\left(x \right)}\right)^{3}}{x^{2} \left(x + 1\right)^{2} \sin^{2}{\left(x \right)}}}{8 \left(x + 1\right) \sin{\left(x \right)}} + \frac{3 \sqrt{x \left(x + 1\right) \sin{\left(x \right)}} \left(x - 2\right) \left(x \left(x + 1\right) \cos{\left(x \right)} + \left(2 x + 1\right) \sin{\left(x \right)}\right)}{2 x \left(x + 1\right) \sin{\left(x \right)}} - \frac{3 \left(x - 1\right) \left(- \frac{2 \sqrt{x \left(x + 1\right) \sin{\left(x \right)}} \left(x \left(x + 1\right) \cos{\left(x \right)} + \left(2 x + 1\right) \sin{\left(x \right)}\right) \cos{\left(x \right)}}{\sin{\left(x \right)}} + 2 \sqrt{x \left(x + 1\right) \sin{\left(x \right)}} \left(- x \left(x + 1\right) \sin{\left(x \right)} + 2 \left(2 x + 1\right) \cos{\left(x \right)} + 2 \sin{\left(x \right)}\right) + \left(x \left(x + 1\right) \cos{\left(x \right)} + \left(2 x + 1\right) \sin{\left(x \right)}\right)^{2} - \frac{2 \sqrt{x \left(x + 1\right) \sin{\left(x \right)}} \left(2 x + 1\right) \left(x \left(x + 1\right) \cos{\left(x \right)} + \left(2 x + 1\right) \sin{\left(x \right)}\right)}{x \left(x + 1\right)} + \frac{\sqrt{x \left(x + 1\right) \sin{\left(x \right)}} \left(x \left(x + 1\right) \cos{\left(x \right)} + \left(2 x + 1\right) \sin{\left(x \right)}\right)^{2}}{x \left(x + 1\right) \sin{\left(x \right)}}\right)}{4 x \left(x + 1\right) \sin{\left(x \right)}}\right) e^{- x} e^{\sqrt{x \left(x + 1\right) \sin{\left(x \right)}}}$$
Gráfico