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 1/t
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Derivada de x^(2/5)
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Derivada de 1/ln(x)
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Derivada de f(x)=√x
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Expresiones idénticas
- x^x^sinx^ tres
- x en el grado x en el grado seno de x al cubo
- x en el grado x en el grado seno de x en el grado tres
- xxsinx3
- x^x^sinx³
- x en el grado x en el grado sinx en el grado 3
Derivada de x^x^sinx^3
Solución
Solución detallada
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Respuesta:
Primera derivada
[src]
/ 3 \ / 3 \
| sin (x)| | sin (x) 3 / 3 \ |
\x / |x sin (x) |sin (x) 2 | |
x *|-------- + x *|------- + 3*sin (x)*cos(x)*log(x)|*log(x)|
\ x \ x / /
$$x^{x^{\sin^{3}{\left(x \right)}}} \left(x^{\sin^{3}{\left(x \right)}} \left(3 \log{\left(x \right)} \sin^{2}{\left(x \right)} \cos{\left(x \right)} + \frac{\sin^{3}{\left(x \right)}}{x}\right) \log{\left(x \right)} + \frac{x^{\sin^{3}{\left(x \right)}}}{x}\right)$$
Segunda derivada
[src]
/ 3 \ / 2 /sin(x) \\
| sin (x)| 3 | 3 2 2 / 2 \ 2*sin (x)*|------ + 3*cos(x)*log(x)||
\x / sin (x) | 1 sin (x) /1 2 /sin(x) \ \ /sin(x) \ 4 |sin (x) 2 2 6*cos(x)*sin(x)| \ x /|
x *x *|- -- + x *|- + sin (x)*|------ + 3*cos(x)*log(x)|*log(x)| + |------ + 3*cos(x)*log(x)| *sin (x)*log(x) - |------- - 6*cos (x)*log(x) + 3*sin (x)*log(x) - ---------------|*log(x)*sin(x) + ------------------------------------|
| 2 \x \ x / / \ x / | 2 x | x |
\ x \ x / /
$$x^{x^{\sin^{3}{\left(x \right)}}} x^{\sin^{3}{\left(x \right)}} \left(x^{\sin^{3}{\left(x \right)}} \left(\left(3 \log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right) \log{\left(x \right)} \sin^{2}{\left(x \right)} + \frac{1}{x}\right)^{2} + \left(3 \log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right)^{2} \log{\left(x \right)} \sin^{4}{\left(x \right)} - \left(3 \log{\left(x \right)} \sin^{2}{\left(x \right)} - 6 \log{\left(x \right)} \cos^{2}{\left(x \right)} - \frac{6 \sin{\left(x \right)} \cos{\left(x \right)}}{x} + \frac{\sin^{2}{\left(x \right)}}{x^{2}}\right) \log{\left(x \right)} \sin{\left(x \right)} + \frac{2 \left(3 \log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right) \sin^{2}{\left(x \right)}}{x} - \frac{1}{x^{2}}\right)$$
Tercera derivada
[src]
/ / 2 \ \
| |sin (x) 2 2 6*cos(x)*sin(x)| 2 |
/ 3 \ | 3*|------- - 6*cos (x)*log(x) + 3*sin (x)*log(x) - ---------------|*sin(x) 2 /sin(x) \ /sin(x) \ 4 / 2 /sin(x) \\ |
| sin (x)| 3 | 3 3 / 3 3 2 2 \ 3 | 2 x | 3*sin (x)*|------ + 3*cos(x)*log(x)| 3*|------ + 3*cos(x)*log(x)| *sin (x) 3 | 2 / 2 \ 2*sin (x)*|------ + 3*cos(x)*log(x)|| / 2 \ |
\x / sin (x) |2 2*sin (x) /1 2 /sin(x) \ \ | 3 2*sin (x) 9*sin (x) 18*cos (x)*sin(x) 9*sin (x)*cos(x) 2 | /sin(x) \ 6 \ x / \ x / \ x / sin (x) /1 2 /sin(x) \ \ | 1 /sin(x) \ 4 |sin (x) 2 2 6*cos(x)*sin(x)| \ x /| 3 /sin(x) \ |sin (x) 2 2 6*cos(x)*sin(x)| |
x *x *|-- + x *|- + sin (x)*|------ + 3*cos(x)*log(x)|*log(x)| - |- 6*cos (x)*log(x) - --------- + --------- - ----------------- + ---------------- + 21*sin (x)*cos(x)*log(x)|*log(x) + |------ + 3*cos(x)*log(x)| *sin (x)*log(x) - -------------------------------------------------------------------------- - ------------------------------------ + ------------------------------------- + 3*x *|- + sin (x)*|------ + 3*cos(x)*log(x)|*log(x)|*|- -- + |------ + 3*cos(x)*log(x)| *sin (x)*log(x) - |------- - 6*cos (x)*log(x) + 3*sin (x)*log(x) - ---------------|*log(x)*sin(x) + ------------------------------------| - 3*sin (x)*|------ + 3*cos(x)*log(x)|*|------- - 6*cos (x)*log(x) + 3*sin (x)*log(x) - ---------------|*log(x)|
| 3 \x \ x / / | 3 x x 2 | \ x / x 2 x \x \ x / / | 2 \ x / | 2 x | x | \ x / | 2 x | |
\x \ x x / x \ x \ x / / \ x / /
$$x^{x^{\sin^{3}{\left(x \right)}}} x^{\sin^{3}{\left(x \right)}} \left(x^{2 \sin^{3}{\left(x \right)}} \left(\left(3 \log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right) \log{\left(x \right)} \sin^{2}{\left(x \right)} + \frac{1}{x}\right)^{3} + 3 x^{\sin^{3}{\left(x \right)}} \left(\left(3 \log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right) \log{\left(x \right)} \sin^{2}{\left(x \right)} + \frac{1}{x}\right) \left(\left(3 \log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right)^{2} \log{\left(x \right)} \sin^{4}{\left(x \right)} - \left(3 \log{\left(x \right)} \sin^{2}{\left(x \right)} - 6 \log{\left(x \right)} \cos^{2}{\left(x \right)} - \frac{6 \sin{\left(x \right)} \cos{\left(x \right)}}{x} + \frac{\sin^{2}{\left(x \right)}}{x^{2}}\right) \log{\left(x \right)} \sin{\left(x \right)} + \frac{2 \left(3 \log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right) \sin^{2}{\left(x \right)}}{x} - \frac{1}{x^{2}}\right) + \left(3 \log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right)^{3} \log{\left(x \right)} \sin^{6}{\left(x \right)} - 3 \left(3 \log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right) \left(3 \log{\left(x \right)} \sin^{2}{\left(x \right)} - 6 \log{\left(x \right)} \cos^{2}{\left(x \right)} - \frac{6 \sin{\left(x \right)} \cos{\left(x \right)}}{x} + \frac{\sin^{2}{\left(x \right)}}{x^{2}}\right) \log{\left(x \right)} \sin^{3}{\left(x \right)} - \left(21 \log{\left(x \right)} \sin^{2}{\left(x \right)} \cos{\left(x \right)} - 6 \log{\left(x \right)} \cos^{3}{\left(x \right)} + \frac{9 \sin^{3}{\left(x \right)}}{x} - \frac{18 \sin{\left(x \right)} \cos^{2}{\left(x \right)}}{x} + \frac{9 \sin^{2}{\left(x \right)} \cos{\left(x \right)}}{x^{2}} - \frac{2 \sin^{3}{\left(x \right)}}{x^{3}}\right) \log{\left(x \right)} + \frac{3 \left(3 \log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right)^{2} \sin^{4}{\left(x \right)}}{x} - \frac{3 \left(3 \log{\left(x \right)} \sin^{2}{\left(x \right)} - 6 \log{\left(x \right)} \cos^{2}{\left(x \right)} - \frac{6 \sin{\left(x \right)} \cos{\left(x \right)}}{x} + \frac{\sin^{2}{\left(x \right)}}{x^{2}}\right) \sin{\left(x \right)}}{x} - \frac{3 \left(3 \log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right) \sin^{2}{\left(x \right)}}{x^{2}} + \frac{2}{x^{3}}\right)$$
Gráfico