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^sinx^x
- x en el grado seno de x en el grado x
- xsinxx
Derivada de x^sinx^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 \
sin (x) |sin (x) x /x*cos(x) \ |
x *|------- + sin (x)*|-------- + log(sin(x))|*log(x)|
\ x \ sin(x) / /
$$x^{\sin^{x}{\left(x \right)}} \left(\left(\frac{x \cos{\left(x \right)}}{\sin{\left(x \right)}} + \log{\left(\sin{\left(x \right)} \right)}\right) \log{\left(x \right)} \sin^{x}{\left(x \right)} + \frac{\sin^{x}{\left(x \right)}}{x}\right)$$
Segunda derivada
[src]
/ /x*cos(x) \\
x | 2 2 / 2 \ 2*|-------- + log(sin(x))||
sin (x) x | 1 /1 /x*cos(x) \ \ x /x*cos(x) \ | 2*cos(x) x*cos (x)| \ sin(x) /|
x *sin (x)*|- -- + |- + |-------- + log(sin(x))|*log(x)| *sin (x) + |-------- + log(sin(x))| *log(x) - |x - -------- + ---------|*log(x) + --------------------------|
| 2 \x \ sin(x) / / \ sin(x) / | sin(x) 2 | x |
\ x \ sin (x) / /
$$x^{\sin^{x}{\left(x \right)}} \left(\left(\left(\frac{x \cos{\left(x \right)}}{\sin{\left(x \right)}} + \log{\left(\sin{\left(x \right)} \right)}\right) \log{\left(x \right)} + \frac{1}{x}\right)^{2} \sin^{x}{\left(x \right)} + \left(\frac{x \cos{\left(x \right)}}{\sin{\left(x \right)}} + \log{\left(\sin{\left(x \right)} \right)}\right)^{2} \log{\left(x \right)} - \left(x + \frac{x \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} - \frac{2 \cos{\left(x \right)}}{\sin{\left(x \right)}}\right) \log{\left(x \right)} + \frac{2 \left(\frac{x \cos{\left(x \right)}}{\sin{\left(x \right)}} + \log{\left(\sin{\left(x \right)} \right)}\right)}{x} - \frac{1}{x^{2}}\right) \sin^{x}{\left(x \right)}$$
Tercera derivada
[src]
/ / 2 \ \
| | 2*cos(x) x*cos (x)| 2 |
| 3*|x - -------- + ---------| /x*cos(x) \ /x*cos(x) \ / /x*cos(x) \\|
x | 3 3 / 2 3 \ | sin(x) 2 | 3*|-------- + log(sin(x))| 3*|-------- + log(sin(x))| / 2 \ | 2 / 2 \ 2*|-------- + log(sin(x))|||
sin (x) x |2 /1 /x*cos(x) \ \ 2*x /x*cos(x) \ | 3*cos (x) 2*x*cos (x) 2*x*cos(x)| \ sin (x) / \ sin(x) / \ sin(x) / /x*cos(x) \ | 2*cos(x) x*cos (x)| x /1 /x*cos(x) \ \ | 1 /x*cos(x) \ | 2*cos(x) x*cos (x)| \ sin(x) /||
x *sin (x)*|-- + |- + |-------- + log(sin(x))|*log(x)| *sin (x) + |-------- + log(sin(x))| *log(x) + |-3 - --------- + ----------- + ----------|*log(x) - ---------------------------- - -------------------------- + --------------------------- - 3*|-------- + log(sin(x))|*|x - -------- + ---------|*log(x) + 3*sin (x)*|- + |-------- + log(sin(x))|*log(x)|*|- -- + |-------- + log(sin(x))| *log(x) - |x - -------- + ---------|*log(x) + --------------------------||
| 3 \x \ sin(x) / / \ sin(x) / | 2 3 sin(x) | x 2 x \ sin(x) / | sin(x) 2 | \x \ sin(x) / / | 2 \ sin(x) / | sin(x) 2 | x ||
\x \ sin (x) sin (x) / x \ sin (x) / \ x \ sin (x) / //
$$x^{\sin^{x}{\left(x \right)}} \left(\left(\left(\frac{x \cos{\left(x \right)}}{\sin{\left(x \right)}} + \log{\left(\sin{\left(x \right)} \right)}\right) \log{\left(x \right)} + \frac{1}{x}\right)^{3} \sin^{2 x}{\left(x \right)} + 3 \left(\left(\frac{x \cos{\left(x \right)}}{\sin{\left(x \right)}} + \log{\left(\sin{\left(x \right)} \right)}\right) \log{\left(x \right)} + \frac{1}{x}\right) \left(\left(\frac{x \cos{\left(x \right)}}{\sin{\left(x \right)}} + \log{\left(\sin{\left(x \right)} \right)}\right)^{2} \log{\left(x \right)} - \left(x + \frac{x \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} - \frac{2 \cos{\left(x \right)}}{\sin{\left(x \right)}}\right) \log{\left(x \right)} + \frac{2 \left(\frac{x \cos{\left(x \right)}}{\sin{\left(x \right)}} + \log{\left(\sin{\left(x \right)} \right)}\right)}{x} - \frac{1}{x^{2}}\right) \sin^{x}{\left(x \right)} + \left(\frac{x \cos{\left(x \right)}}{\sin{\left(x \right)}} + \log{\left(\sin{\left(x \right)} \right)}\right)^{3} \log{\left(x \right)} - 3 \left(\frac{x \cos{\left(x \right)}}{\sin{\left(x \right)}} + \log{\left(\sin{\left(x \right)} \right)}\right) \left(x + \frac{x \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} - \frac{2 \cos{\left(x \right)}}{\sin{\left(x \right)}}\right) \log{\left(x \right)} + \left(\frac{2 x \cos{\left(x \right)}}{\sin{\left(x \right)}} + \frac{2 x \cos^{3}{\left(x \right)}}{\sin^{3}{\left(x \right)}} - 3 - \frac{3 \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) \log{\left(x \right)} + \frac{3 \left(\frac{x \cos{\left(x \right)}}{\sin{\left(x \right)}} + \log{\left(\sin{\left(x \right)} \right)}\right)^{2}}{x} - \frac{3 \left(x + \frac{x \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} - \frac{2 \cos{\left(x \right)}}{\sin{\left(x \right)}}\right)}{x} - \frac{3 \left(\frac{x \cos{\left(x \right)}}{\sin{\left(x \right)}} + \log{\left(\sin{\left(x \right)} \right)}\right)}{x^{2}} + \frac{2}{x^{3}}\right) \sin^{x}{\left(x \right)}$$