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
- (аrctgx)^tgx
- (аrctgx) en el grado tgx
- (аrctgx)tgx
- аrctgxtgx
- аrctgx^tgx
Derivada de (аrctgx)^tgx
Solución
Ha introducido
[src]
tan(x) acot (x)
$$\operatorname{acot}^{\tan{\left(x \right)}}{\left(x \right)}$$
acot(x)^tan(x)
Solución detallada
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Respuesta:
Primera derivada
[src]
tan(x) // 2 \ tan(x) \
acot (x)*|\1 + tan (x)/*log(acot(x)) - ----------------|
| / 2\ |
\ \1 + x /*acot(x)/
$$\left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(\operatorname{acot}{\left(x \right)} \right)} - \frac{\tan{\left(x \right)}}{\left(x^{2} + 1\right) \operatorname{acot}{\left(x \right)}}\right) \operatorname{acot}^{\tan{\left(x \right)}}{\left(x \right)}$$
Segunda derivada
[src]
/ 2 / 2 \ \
tan(x) |// 2 \ tan(x) \ tan(x) 2*\1 + tan (x)/ / 2 \ 2*x*tan(x) |
acot (x)*||\1 + tan (x)/*log(acot(x)) - ----------------| - ------------------ - ---------------- + 2*\1 + tan (x)/*log(acot(x))*tan(x) + -----------------|
|| / 2\ | 2 / 2\ 2 |
|\ \1 + x /*acot(x)/ / 2\ 2 \1 + x /*acot(x) / 2\ |
\ \1 + x / *acot (x) \1 + x / *acot(x)/
$$\left(\frac{2 x \tan{\left(x \right)}}{\left(x^{2} + 1\right)^{2} \operatorname{acot}{\left(x \right)}} + \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(\operatorname{acot}{\left(x \right)} \right)} - \frac{\tan{\left(x \right)}}{\left(x^{2} + 1\right) \operatorname{acot}{\left(x \right)}}\right)^{2} + 2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(\operatorname{acot}{\left(x \right)} \right)} \tan{\left(x \right)} - \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)}{\left(x^{2} + 1\right) \operatorname{acot}{\left(x \right)}} - \frac{\tan{\left(x \right)}}{\left(x^{2} + 1\right)^{2} \operatorname{acot}^{2}{\left(x \right)}}\right) \operatorname{acot}^{\tan{\left(x \right)}}{\left(x \right)}$$
Tercera derivada
[src]
/ 3 2 / / 2 \ \ / 2 \ 2 / 2 \ / 2 \\
tan(x) |// 2 \ tan(x) \ / 2 \ // 2 \ tan(x) \ | tan(x) 2*\1 + tan (x)/ / 2 \ 2*x*tan(x) | 3*\1 + tan (x)/ 2*tan(x) 2*tan(x) 2 / 2 \ 8*x *tan(x) 6*\1 + tan (x)/*tan(x) 6*x*tan(x) 6*x*\1 + tan (x)/|
acot (x)*||\1 + tan (x)/*log(acot(x)) - ----------------| + 2*\1 + tan (x)/ *log(acot(x)) + 3*|\1 + tan (x)/*log(acot(x)) - ----------------|*|- ------------------ - ---------------- + 2*\1 + tan (x)/*log(acot(x))*tan(x) + -----------------| - ------------------ - ------------------ + ----------------- + 4*tan (x)*\1 + tan (x)/*log(acot(x)) - ----------------- - ---------------------- + ------------------ + -----------------|
|| / 2\ | | / 2\ | | 2 / 2\ 2 | 2 3 2 3 / 2\ 3 2 |
|\ \1 + x /*acot(x)/ \ \1 + x /*acot(x)/ | / 2\ 2 \1 + x /*acot(x) / 2\ | / 2\ 2 / 2\ 3 / 2\ / 2\ \1 + x /*acot(x) / 2\ 2 / 2\ |
\ \ \1 + x / *acot (x) \1 + x / *acot(x)/ \1 + x / *acot (x) \1 + x / *acot (x) \1 + x / *acot(x) \1 + x / *acot(x) \1 + x / *acot (x) \1 + x / *acot(x)/
$$\left(- \frac{8 x^{2} \tan{\left(x \right)}}{\left(x^{2} + 1\right)^{3} \operatorname{acot}{\left(x \right)}} + \frac{6 x \left(\tan^{2}{\left(x \right)} + 1\right)}{\left(x^{2} + 1\right)^{2} \operatorname{acot}{\left(x \right)}} + \frac{6 x \tan{\left(x \right)}}{\left(x^{2} + 1\right)^{3} \operatorname{acot}^{2}{\left(x \right)}} + \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(\operatorname{acot}{\left(x \right)} \right)} - \frac{\tan{\left(x \right)}}{\left(x^{2} + 1\right) \operatorname{acot}{\left(x \right)}}\right)^{3} + 3 \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(\operatorname{acot}{\left(x \right)} \right)} - \frac{\tan{\left(x \right)}}{\left(x^{2} + 1\right) \operatorname{acot}{\left(x \right)}}\right) \left(\frac{2 x \tan{\left(x \right)}}{\left(x^{2} + 1\right)^{2} \operatorname{acot}{\left(x \right)}} + 2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(\operatorname{acot}{\left(x \right)} \right)} \tan{\left(x \right)} - \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)}{\left(x^{2} + 1\right) \operatorname{acot}{\left(x \right)}} - \frac{\tan{\left(x \right)}}{\left(x^{2} + 1\right)^{2} \operatorname{acot}^{2}{\left(x \right)}}\right) + 2 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \log{\left(\operatorname{acot}{\left(x \right)} \right)} + 4 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(\operatorname{acot}{\left(x \right)} \right)} \tan^{2}{\left(x \right)} - \frac{6 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}}{\left(x^{2} + 1\right) \operatorname{acot}{\left(x \right)}} - \frac{3 \left(\tan^{2}{\left(x \right)} + 1\right)}{\left(x^{2} + 1\right)^{2} \operatorname{acot}^{2}{\left(x \right)}} + \frac{2 \tan{\left(x \right)}}{\left(x^{2} + 1\right)^{2} \operatorname{acot}{\left(x \right)}} - \frac{2 \tan{\left(x \right)}}{\left(x^{2} + 1\right)^{3} \operatorname{acot}^{3}{\left(x \right)}}\right) \operatorname{acot}^{\tan{\left(x \right)}}{\left(x \right)}$$
Gráfico