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*sin(x))^x
- (x multiplicar por seno de (x)) en el grado x
- (x*sin(x))x
- x*sinxx
- (xsin(x))^x
- (xsin(x))x
- xsinxx
- xsinx^x
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Expresiones semejantes
- (x*sinx)^x
Derivada de (x*sin(x))^x
Solución
Solución detallada
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Respuesta:
Primera derivada
[src]
x /x*cos(x) + sin(x) \
(x*sin(x)) *|----------------- + log(x*sin(x))|
\ sin(x) /
$$\left(x \sin{\left(x \right)}\right)^{x} \left(\frac{x \cos{\left(x \right)} + \sin{\left(x \right)}}{\sin{\left(x \right)}} + \log{\left(x \sin{\left(x \right)} \right)}\right)$$
Segunda derivada
[src]
/ x*cos(x) + sin(x) (x*cos(x) + sin(x))*cos(x)\
| 2 -2*cos(x) + x*sin(x) - ----------------- + --------------------------|
x |/x*cos(x) + sin(x) \ x sin(x) |
(x*sin(x)) *||----------------- + log(x*sin(x))| - ---------------------------------------------------------------------|
\\ sin(x) / sin(x) /
$$\left(x \sin{\left(x \right)}\right)^{x} \left(\left(\frac{x \cos{\left(x \right)} + \sin{\left(x \right)}}{\sin{\left(x \right)}} + \log{\left(x \sin{\left(x \right)} \right)}\right)^{2} - \frac{x \sin{\left(x \right)} + \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \cos{\left(x \right)}}{\sin{\left(x \right)}} - 2 \cos{\left(x \right)} - \frac{x \cos{\left(x \right)} + \sin{\left(x \right)}}{x}}{\sin{\left(x \right)}}\right)$$
Tercera derivada
[src]
/ 2 \
| -2*cos(x) + x*sin(x) x*cos(x) + sin(x) 2*cos (x)*(x*cos(x) + sin(x)) 2*(-2*cos(x) + x*sin(x))*cos(x) (x*cos(x) + sin(x))*cos(x) |
| 2*sin(x) + -------------------- + ----------------- - ----------------------------- - ------------------------------- + -------------------------- /x*cos(x) + sin(x) \ / x*cos(x) + sin(x) (x*cos(x) + sin(x))*cos(x)\|
| 3 x 2 2 sin(x) x*sin(x) 3*|----------------- + log(x*sin(x))|*|-2*cos(x) + x*sin(x) - ----------------- + --------------------------||
x |/x*cos(x) + sin(x) \ x sin (x) \ sin(x) / \ x sin(x) /|
(x*sin(x)) *||----------------- + log(x*sin(x))| - -------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------|
\\ sin(x) / sin(x) sin(x) /
$$\left(x \sin{\left(x \right)}\right)^{x} \left(\left(\frac{x \cos{\left(x \right)} + \sin{\left(x \right)}}{\sin{\left(x \right)}} + \log{\left(x \sin{\left(x \right)} \right)}\right)^{3} - \frac{3 \left(\frac{x \cos{\left(x \right)} + \sin{\left(x \right)}}{\sin{\left(x \right)}} + \log{\left(x \sin{\left(x \right)} \right)}\right) \left(x \sin{\left(x \right)} + \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \cos{\left(x \right)}}{\sin{\left(x \right)}} - 2 \cos{\left(x \right)} - \frac{x \cos{\left(x \right)} + \sin{\left(x \right)}}{x}\right)}{\sin{\left(x \right)}} - \frac{- \frac{2 \left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \cos{\left(x \right)}}{\sin{\left(x \right)}} - \frac{2 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} + 2 \sin{\left(x \right)} + \frac{x \sin{\left(x \right)} - 2 \cos{\left(x \right)}}{x} + \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \cos{\left(x \right)}}{x \sin{\left(x \right)}} + \frac{x \cos{\left(x \right)} + \sin{\left(x \right)}}{x^{2}}}{\sin{\left(x \right)}}\right)$$
Gráfico