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 x^2sinx
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Derivada de y
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Derivada de 1/(x+1)^2
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Derivada de u
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Expresiones idénticas
- y= tres ^x^ dos ^tgx
- y es igual a 3 en el grado x al cuadrado en el grado tgx
- y es igual a tres en el grado x en el grado dos en el grado tgx
- y=3x2tgx
- y=3^x²^tgx
- y=3 en el grado x en el grado 2 en el grado tgx
Derivada de y=3^x^2^tgx
Solución
Ha introducido
[src]
/ / tan(x)\\ | \2 /| \x / 3
$$3^{x^{2^{\tan{\left(x \right)}}}}$$
3^(x^(2^tan(x)))
Solución detallada
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Sustituimos .
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Luego se aplica una cadena de reglas. Multiplicamos por :
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Como resultado de la secuencia de reglas:
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Simplificamos:
Respuesta:
Primera derivada
[src]
/ / tan(x)\\
| \2 /| / tan(x)\ / tan(x) \
\x / \2 / |2 tan(x) / 2 \ |
3 *x *|------- + 2 *\1 + tan (x)/*log(2)*log(x)|*log(3)
\ x /
$$3^{x^{2^{\tan{\left(x \right)}}}} x^{2^{\tan{\left(x \right)}}} \left(2^{\tan{\left(x \right)}} \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(2 \right)} \log{\left(x \right)} + \frac{2^{\tan{\left(x \right)}}}{x}\right) \log{\left(3 \right)}$$
Segunda derivada
[src]
/ / tan(x)\\
| \2 /| / tan(x)\ / 2 2 / 2 \ / tan(x)\ 2 \
tan(x) \x / \2 / | 1 tan(x) /1 / 2 \ \ / 2 \ 2 2*\1 + tan (x)/*log(2) tan(x) \2 / /1 / 2 \ \ / 2 \ |
2 *3 *x *|- -- + 2 *|- + \1 + tan (x)/*log(2)*log(x)| + \1 + tan (x)/ *log (2)*log(x) + ---------------------- + 2 *x *|- + \1 + tan (x)/*log(2)*log(x)| *log(3) + 2*\1 + tan (x)/*log(2)*log(x)*tan(x)|*log(3)
| 2 \x / x \x / |
\ x /
$$2^{\tan{\left(x \right)}} 3^{x^{2^{\tan{\left(x \right)}}}} x^{2^{\tan{\left(x \right)}}} \left(2^{\tan{\left(x \right)}} x^{2^{\tan{\left(x \right)}}} \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(2 \right)} \log{\left(x \right)} + \frac{1}{x}\right)^{2} \log{\left(3 \right)} + 2^{\tan{\left(x \right)}} \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(2 \right)} \log{\left(x \right)} + \frac{1}{x}\right)^{2} + \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \log{\left(2 \right)}^{2} \log{\left(x \right)} + 2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(2 \right)} \log{\left(x \right)} \tan{\left(x \right)} + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(2 \right)}}{x} - \frac{1}{x^{2}}\right) \log{\left(3 \right)}$$
Tercera derivada
[src]
/ / tan(x)\\ / 2 \
| \2 /| / tan(x)\ | 3 3 / 2 \ 2 / 2 / 2 \ \ / 2 \ 2 tan(x) 3 / tan(x)\ 3 / 2 \ 2 / tan(x)\ / 2 / 2 \ \ |
tan(x) \x / \2 / |2 2*tan(x) /1 / 2 \ \ / 2 \ 3 3*\1 + tan (x)/*log(2) / 2 \ tan(x) /1 / 2 \ \ | 1 / 2 \ 2 2*\1 + tan (x)/*log(2) / 2 \ | 3*\1 + tan (x)/ *log (2) 2*tan(x) 2*2 /1 / 2 \ \ 2 2*tan(x) \2 / /1 / 2 \ \ 2 / 2 \ 6*\1 + tan (x)/*log(2)*tan(x) / 2 \ 2 tan(x) \2 / /1 / 2 \ \ | 1 / 2 \ 2 2*\1 + tan (x)/*log(2) / 2 \ | |
2 *3 *x *|-- + 2 *|- + \1 + tan (x)/*log(2)*log(x)| + \1 + tan (x)/ *log (2)*log(x) - ---------------------- + 2*\1 + tan (x)/ *log(2)*log(x) + 3*2 *|- + \1 + tan (x)/*log(2)*log(x)|*|- -- + \1 + tan (x)/ *log (2)*log(x) + ---------------------- + 2*\1 + tan (x)/*log(2)*log(x)*tan(x)| + ------------------------ + 2 *x *|- + \1 + tan (x)/*log(2)*log(x)| *log (3) + 3*2 *x *|- + \1 + tan (x)/*log(2)*log(x)| *log(3) + 4*tan (x)*\1 + tan (x)/*log(2)*log(x) + ----------------------------- + 6*\1 + tan (x)/ *log (2)*log(x)*tan(x) + 3*2 *x *|- + \1 + tan (x)/*log(2)*log(x)|*|- -- + \1 + tan (x)/ *log (2)*log(x) + ---------------------- + 2*\1 + tan (x)/*log(2)*log(x)*tan(x)|*log(3)|*log(3)
| 3 \x / 2 \x / | 2 x | x \x / \x / x \x / | 2 x | |
\x x \ x / \ x / /
$$2^{\tan{\left(x \right)}} 3^{x^{2^{\tan{\left(x \right)}}}} x^{2^{\tan{\left(x \right)}}} \left(2^{2 \tan{\left(x \right)}} x^{2 \cdot 2^{\tan{\left(x \right)}}} \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(2 \right)} \log{\left(x \right)} + \frac{1}{x}\right)^{3} \log{\left(3 \right)}^{2} + 3 \cdot 2^{2 \tan{\left(x \right)}} x^{2^{\tan{\left(x \right)}}} \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(2 \right)} \log{\left(x \right)} + \frac{1}{x}\right)^{3} \log{\left(3 \right)} + 2^{2 \tan{\left(x \right)}} \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(2 \right)} \log{\left(x \right)} + \frac{1}{x}\right)^{3} + 3 \cdot 2^{\tan{\left(x \right)}} x^{2^{\tan{\left(x \right)}}} \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(2 \right)} \log{\left(x \right)} + \frac{1}{x}\right) \left(\left(\tan^{2}{\left(x \right)} + 1\right)^{2} \log{\left(2 \right)}^{2} \log{\left(x \right)} + 2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(2 \right)} \log{\left(x \right)} \tan{\left(x \right)} + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(2 \right)}}{x} - \frac{1}{x^{2}}\right) \log{\left(3 \right)} + 3 \cdot 2^{\tan{\left(x \right)}} \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(2 \right)} \log{\left(x \right)} + \frac{1}{x}\right) \left(\left(\tan^{2}{\left(x \right)} + 1\right)^{2} \log{\left(2 \right)}^{2} \log{\left(x \right)} + 2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(2 \right)} \log{\left(x \right)} \tan{\left(x \right)} + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(2 \right)}}{x} - \frac{1}{x^{2}}\right) + \left(\tan^{2}{\left(x \right)} + 1\right)^{3} \log{\left(2 \right)}^{3} \log{\left(x \right)} + 6 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \log{\left(2 \right)}^{2} \log{\left(x \right)} \tan{\left(x \right)} + 2 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \log{\left(2 \right)} \log{\left(x \right)} + 4 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(2 \right)} \log{\left(x \right)} \tan^{2}{\left(x \right)} + \frac{3 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \log{\left(2 \right)}^{2}}{x} + \frac{6 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(2 \right)} \tan{\left(x \right)}}{x} - \frac{3 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(2 \right)}}{x^{2}} + \frac{2}{x^{3}}\right) \log{\left(3 \right)}$$