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/(x+3)
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Derivada de 4*y
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Derivada de (2x-7)^8
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Derivada de (-1)/x-3*x
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Expresiones idénticas
- y=(tg(x))^(arctg(x))
- y es igual a (tg(x)) en el grado (arctg(x))
- y=(tg(x))(arctg(x))
- y=tgxarctgx
- y=tgx^arctgx
Derivada de y=(tg(x))^(arctg(x))
Solución
Ha introducido
[src]
atan(x) tan (x)
$$\tan^{\operatorname{atan}{\left(x \right)}}{\left(x \right)}$$
tan(x)^atan(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 \ \
atan(x) |log(tan(x)) \1 + tan (x)/*atan(x)|
tan (x)*|----------- + ---------------------|
| 2 tan(x) |
\ 1 + x /
$$\left(\frac{\left(\tan^{2}{\left(x \right)} + 1\right) \operatorname{atan}{\left(x \right)}}{\tan{\left(x \right)}} + \frac{\log{\left(\tan{\left(x \right)} \right)}}{x^{2} + 1}\right) \tan^{\operatorname{atan}{\left(x \right)}}{\left(x \right)}$$
Segunda derivada
[src]
/ 2 2 \
|/ / 2 \ \ / 2 \ / 2 \|
atan(x) ||log(tan(x)) \1 + tan (x)/*atan(x)| / 2 \ \1 + tan (x)/ *atan(x) 2*x*log(tan(x)) 2*\1 + tan (x)/|
tan (x)*||----------- + ---------------------| + 2*\1 + tan (x)/*atan(x) - ---------------------- - --------------- + ---------------|
|| 2 tan(x) | 2 2 / 2\ |
|\ 1 + x / tan (x) / 2\ \1 + x /*tan(x)|
\ \1 + x / /
$$\left(- \frac{2 x \log{\left(\tan{\left(x \right)} \right)}}{\left(x^{2} + 1\right)^{2}} + \left(\frac{\left(\tan^{2}{\left(x \right)} + 1\right) \operatorname{atan}{\left(x \right)}}{\tan{\left(x \right)}} + \frac{\log{\left(\tan{\left(x \right)} \right)}}{x^{2} + 1}\right)^{2} - \frac{\left(\tan^{2}{\left(x \right)} + 1\right)^{2} \operatorname{atan}{\left(x \right)}}{\tan^{2}{\left(x \right)}} + 2 \left(\tan^{2}{\left(x \right)} + 1\right) \operatorname{atan}{\left(x \right)} + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)}{\left(x^{2} + 1\right) \tan{\left(x \right)}}\right) \tan^{\operatorname{atan}{\left(x \right)}}{\left(x \right)}$$
Tercera derivada
[src]
/ 3 / 2 \ 2 2 3 \
|/ / 2 \ \ / / 2 \ \ | / 2 \ / 2 \ | / 2 \ / 2 \ / 2 \ / 2 \ 2 / 2 \|
atan(x) ||log(tan(x)) \1 + tan (x)/*atan(x)| |log(tan(x)) \1 + tan (x)/*atan(x)| | / 2 \ \1 + tan (x)/ *atan(x) 2*\1 + tan (x)/ 2*x*log(tan(x))| 2*log(tan(x)) 6*\1 + tan (x)/ 4*\1 + tan (x)/ *atan(x) 3*\1 + tan (x)/ 2*\1 + tan (x)/ *atan(x) / 2 \ 8*x *log(tan(x)) 6*x*\1 + tan (x)/|
tan (x)*||----------- + ---------------------| - 3*|----------- + ---------------------|*|- 2*\1 + tan (x)/*atan(x) + ---------------------- - --------------- + ---------------| - ------------- + --------------- - ------------------------ - ---------------- + ------------------------ + 4*\1 + tan (x)/*atan(x)*tan(x) + ---------------- - -----------------|
|| 2 tan(x) | | 2 tan(x) | | 2 / 2\ 2 | 2 2 tan(x) / 2\ 2 3 3 2 |
|\ 1 + x / \ 1 + x / | tan (x) \1 + x /*tan(x) / 2\ | / 2\ 1 + x \1 + x /*tan (x) tan (x) / 2\ / 2\ |
\ \ \1 + x / / \1 + x / \1 + x / \1 + x / *tan(x)/
$$\left(\frac{8 x^{2} \log{\left(\tan{\left(x \right)} \right)}}{\left(x^{2} + 1\right)^{3}} - \frac{6 x \left(\tan^{2}{\left(x \right)} + 1\right)}{\left(x^{2} + 1\right)^{2} \tan{\left(x \right)}} + \left(\frac{\left(\tan^{2}{\left(x \right)} + 1\right) \operatorname{atan}{\left(x \right)}}{\tan{\left(x \right)}} + \frac{\log{\left(\tan{\left(x \right)} \right)}}{x^{2} + 1}\right)^{3} - 3 \left(\frac{\left(\tan^{2}{\left(x \right)} + 1\right) \operatorname{atan}{\left(x \right)}}{\tan{\left(x \right)}} + \frac{\log{\left(\tan{\left(x \right)} \right)}}{x^{2} + 1}\right) \left(\frac{2 x \log{\left(\tan{\left(x \right)} \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{\left(\tan^{2}{\left(x \right)} + 1\right)^{2} \operatorname{atan}{\left(x \right)}}{\tan^{2}{\left(x \right)}} - 2 \left(\tan^{2}{\left(x \right)} + 1\right) \operatorname{atan}{\left(x \right)} - \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)}{\left(x^{2} + 1\right) \tan{\left(x \right)}}\right) + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)^{3} \operatorname{atan}{\left(x \right)}}{\tan^{3}{\left(x \right)}} - \frac{4 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \operatorname{atan}{\left(x \right)}}{\tan{\left(x \right)}} + 4 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} \operatorname{atan}{\left(x \right)} - \frac{3 \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{\left(x^{2} + 1\right) \tan^{2}{\left(x \right)}} + \frac{6 \left(\tan^{2}{\left(x \right)} + 1\right)}{x^{2} + 1} - \frac{2 \log{\left(\tan{\left(x \right)} \right)}}{\left(x^{2} + 1\right)^{2}}\right) \tan^{\operatorname{atan}{\left(x \right)}}{\left(x \right)}$$
Gráfico