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^-7
- Derivada de i*n*x
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Derivada de 5*tan(x)^3+sin(4*x)*e^((-x)/7)
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Derivada de (-2)/x^3
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Expresiones idénticas
- (atan(x))^(log(x))
- ( arco tangente de gente de (x)) en el grado ( logaritmo de (x))
- (atan(x))(log(x))
- atanxlogx
- atanx^logx
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Expresiones semejantes
- (arctan(x))^(log(x))
- (arctanx)^(log(x))
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Expresiones con funciones
- Arcotangente arctan
- atan(x/sqrt(1-x^2))-log(1+x*sqrt(1-x^2))
- atan(2*x+1)/(2*x-1)
- atan(2*x+5)
- atan(e^x)
- atan((x-1)/(x+1))
- Logaritmo log
- log^2(x)
- log2(5x+3)
- log(x+cos(x))^(2)
- log(x*sin(x)+cos(x))
- log((x+1)/(x-1))
Derivada de (atan(x))^(log(x))
Solución
Ha introducido
[src]
log(x) atan (x)
$$\operatorname{atan}^{\log{\left(x \right)}}{\left(x \right)}$$
atan(x)^log(x)
Solución detallada
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Respuesta:
Primera derivada
[src]
log(x) /log(atan(x)) log(x) \
atan (x)*|------------ + ----------------|
| x / 2\ |
\ \1 + x /*atan(x)/
$$\left(\frac{\log{\left(x \right)}}{\left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)}} + \frac{\log{\left(\operatorname{atan}{\left(x \right)} \right)}}{x}\right) \operatorname{atan}^{\log{\left(x \right)}}{\left(x \right)}$$
Segunda derivada
[src]
/ 2 \
log(x) |/log(atan(x)) log(x) \ log(atan(x)) log(x) 2 2*x*log(x) |
atan (x)*||------------ + ----------------| - ------------ - ------------------ + ------------------ - -----------------|
|| x / 2\ | 2 2 / 2\ 2 |
|\ \1 + x /*atan(x)/ x / 2\ 2 x*\1 + x /*atan(x) / 2\ |
\ \1 + x / *atan (x) \1 + x / *atan(x)/
$$\left(- \frac{2 x \log{\left(x \right)}}{\left(x^{2} + 1\right)^{2} \operatorname{atan}{\left(x \right)}} + \left(\frac{\log{\left(x \right)}}{\left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)}} + \frac{\log{\left(\operatorname{atan}{\left(x \right)} \right)}}{x}\right)^{2} - \frac{\log{\left(x \right)}}{\left(x^{2} + 1\right)^{2} \operatorname{atan}^{2}{\left(x \right)}} + \frac{2}{x \left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)}} - \frac{\log{\left(\operatorname{atan}{\left(x \right)} \right)}}{x^{2}}\right) \operatorname{atan}^{\log{\left(x \right)}}{\left(x \right)}$$
Tercera derivada
[src]
/ 3 2 \
log(x) |/log(atan(x)) log(x) \ 6 /log(atan(x)) log(x) \ /log(atan(x)) log(x) 2 2*x*log(x) \ 2*log(atan(x)) 3 3 2*log(x) 2*log(x) 6*x*log(x) 8*x *log(x) |
atan (x)*||------------ + ----------------| - ----------------- - 3*|------------ + ----------------|*|------------ + ------------------ - ------------------ + -----------------| + -------------- - -------------------- - ------------------- - ----------------- + ------------------ + ------------------ + -----------------|
|| x / 2\ | 2 | x / 2\ | | 2 2 / 2\ 2 | 3 2 2 / 2\ 2 3 3 3 |
|\ \1 + x /*atan(x)/ / 2\ \ \1 + x /*atan(x)/ | x / 2\ 2 x*\1 + x /*atan(x) / 2\ | x / 2\ 2 x *\1 + x /*atan(x) / 2\ / 2\ 3 / 2\ 2 / 2\ |
\ \1 + x / *atan(x) \ \1 + x / *atan (x) \1 + x / *atan(x)/ x*\1 + x / *atan (x) \1 + x / *atan(x) \1 + x / *atan (x) \1 + x / *atan (x) \1 + x / *atan(x)/
$$\left(\frac{8 x^{2} \log{\left(x \right)}}{\left(x^{2} + 1\right)^{3} \operatorname{atan}{\left(x \right)}} + \frac{6 x \log{\left(x \right)}}{\left(x^{2} + 1\right)^{3} \operatorname{atan}^{2}{\left(x \right)}} + \left(\frac{\log{\left(x \right)}}{\left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)}} + \frac{\log{\left(\operatorname{atan}{\left(x \right)} \right)}}{x}\right)^{3} - 3 \left(\frac{\log{\left(x \right)}}{\left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)}} + \frac{\log{\left(\operatorname{atan}{\left(x \right)} \right)}}{x}\right) \left(\frac{2 x \log{\left(x \right)}}{\left(x^{2} + 1\right)^{2} \operatorname{atan}{\left(x \right)}} + \frac{\log{\left(x \right)}}{\left(x^{2} + 1\right)^{2} \operatorname{atan}^{2}{\left(x \right)}} - \frac{2}{x \left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)}} + \frac{\log{\left(\operatorname{atan}{\left(x \right)} \right)}}{x^{2}}\right) - \frac{2 \log{\left(x \right)}}{\left(x^{2} + 1\right)^{2} \operatorname{atan}{\left(x \right)}} - \frac{6}{\left(x^{2} + 1\right)^{2} \operatorname{atan}{\left(x \right)}} + \frac{2 \log{\left(x \right)}}{\left(x^{2} + 1\right)^{3} \operatorname{atan}^{3}{\left(x \right)}} - \frac{3}{x \left(x^{2} + 1\right)^{2} \operatorname{atan}^{2}{\left(x \right)}} - \frac{3}{x^{2} \left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)}} + \frac{2 \log{\left(\operatorname{atan}{\left(x \right)} \right)}}{x^{3}}\right) \operatorname{atan}^{\log{\left(x \right)}}{\left(x \right)}$$
Gráfico