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 1/x^5
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Derivada de x*e^(-x^2)
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Derivada de 1/(x+1)^2
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Derivada de x^(4/5)
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Expresiones idénticas
- (x*sin(4x))^(2x)
- (x multiplicar por seno de (4x)) en el grado (2x)
- (x*sin(4x))(2x)
- x*sin4x2x
- (xsin(4x))^(2x)
- (xsin(4x))(2x)
- xsin4x2x
- xsin4x^2x
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Expresiones con funciones
- Seno sin
- sin^3*x
- sin^-1(x)
- sin(x)/((2*x))
- sin(5-3*x)
- sin(x/5)
Derivada de (x*sin(4x))^(2x)
Solución
Ha introducido
[src]
2*x (x*sin(4*x))
$$\left(x \sin{\left(4 x \right)}\right)^{2 x}$$
(x*sin(4*x))^(2*x)
Solución detallada
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Respuesta:
Primera derivada
[src]
2*x / 2*(4*x*cos(4*x) + sin(4*x))\
(x*sin(4*x)) *|2*log(x*sin(4*x)) + ---------------------------|
\ sin(4*x) /
$$\left(x \sin{\left(4 x \right)}\right)^{2 x} \left(\frac{2 \left(4 x \cos{\left(4 x \right)} + \sin{\left(4 x \right)}\right)}{\sin{\left(4 x \right)}} + 2 \log{\left(x \sin{\left(4 x \right)} \right)}\right)$$
Segunda derivada
[src]
/ 4*x*cos(4*x) + sin(4*x) 4*(4*x*cos(4*x) + sin(4*x))*cos(4*x)\
| 2 -8*cos(4*x) - ----------------------- + 16*x*sin(4*x) + ------------------------------------|
2*x | /4*x*cos(4*x) + sin(4*x) \ x sin(4*x) |
2*(x*sin(4*x)) *|2*|----------------------- + log(x*sin(4*x))| - --------------------------------------------------------------------------------------------|
\ \ sin(4*x) / sin(4*x) /
$$2 \left(x \sin{\left(4 x \right)}\right)^{2 x} \left(2 \left(\frac{4 x \cos{\left(4 x \right)} + \sin{\left(4 x \right)}}{\sin{\left(4 x \right)}} + \log{\left(x \sin{\left(4 x \right)} \right)}\right)^{2} - \frac{16 x \sin{\left(4 x \right)} + \frac{4 \left(4 x \cos{\left(4 x \right)} + \sin{\left(4 x \right)}\right) \cos{\left(4 x \right)}}{\sin{\left(4 x \right)}} - 8 \cos{\left(4 x \right)} - \frac{4 x \cos{\left(4 x \right)} + \sin{\left(4 x \right)}}{x}}{\sin{\left(4 x \right)}}\right)$$
Tercera derivada
[src]
/ 2 \
| 4*x*cos(4*x) + sin(4*x) 8*(-cos(4*x) + 2*x*sin(4*x)) 64*(-cos(4*x) + 2*x*sin(4*x))*cos(4*x) 32*cos (4*x)*(4*x*cos(4*x) + sin(4*x)) 4*(4*x*cos(4*x) + sin(4*x))*cos(4*x) |
| 32*sin(4*x) + ----------------------- + ---------------------------- - -------------------------------------- - -------------------------------------- + ------------------------------------ /4*x*cos(4*x) + sin(4*x) \ / 4*x*cos(4*x) + sin(4*x) 4*(4*x*cos(4*x) + sin(4*x))*cos(4*x)\|
| 3 2 x sin(4*x) 2 x*sin(4*x) 6*|----------------------- + log(x*sin(4*x))|*|-8*cos(4*x) - ----------------------- + 16*x*sin(4*x) + ------------------------------------||
2*x | /4*x*cos(4*x) + sin(4*x) \ x sin (4*x) \ sin(4*x) / \ x sin(4*x) /|
2*(x*sin(4*x)) *|4*|----------------------- + log(x*sin(4*x))| - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------|
\ \ sin(4*x) / sin(4*x) sin(4*x) /
$$2 \left(x \sin{\left(4 x \right)}\right)^{2 x} \left(4 \left(\frac{4 x \cos{\left(4 x \right)} + \sin{\left(4 x \right)}}{\sin{\left(4 x \right)}} + \log{\left(x \sin{\left(4 x \right)} \right)}\right)^{3} - \frac{6 \left(\frac{4 x \cos{\left(4 x \right)} + \sin{\left(4 x \right)}}{\sin{\left(4 x \right)}} + \log{\left(x \sin{\left(4 x \right)} \right)}\right) \left(16 x \sin{\left(4 x \right)} + \frac{4 \left(4 x \cos{\left(4 x \right)} + \sin{\left(4 x \right)}\right) \cos{\left(4 x \right)}}{\sin{\left(4 x \right)}} - 8 \cos{\left(4 x \right)} - \frac{4 x \cos{\left(4 x \right)} + \sin{\left(4 x \right)}}{x}\right)}{\sin{\left(4 x \right)}} - \frac{- \frac{64 \left(2 x \sin{\left(4 x \right)} - \cos{\left(4 x \right)}\right) \cos{\left(4 x \right)}}{\sin{\left(4 x \right)}} - \frac{32 \left(4 x \cos{\left(4 x \right)} + \sin{\left(4 x \right)}\right) \cos^{2}{\left(4 x \right)}}{\sin^{2}{\left(4 x \right)}} + 32 \sin{\left(4 x \right)} + \frac{8 \left(2 x \sin{\left(4 x \right)} - \cos{\left(4 x \right)}\right)}{x} + \frac{4 \left(4 x \cos{\left(4 x \right)} + \sin{\left(4 x \right)}\right) \cos{\left(4 x \right)}}{x \sin{\left(4 x \right)}} + \frac{4 x \cos{\left(4 x \right)} + \sin{\left(4 x \right)}}{x^{2}}}{\sin{\left(4 x \right)}}\right)$$
Gráfico