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 6/x
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Derivada de e^(x/2)
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Derivada de 4^x
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Derivada de (sin(x))^x
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Expresiones idénticas
- y=ln^ cuatro (uno -arctg3x)
- y es igual a ln en el grado 4(1 menos arctg3x)
- y es igual a ln en el grado cuatro (uno menos arctg3x)
- y=ln4(1-arctg3x)
- y=ln41-arctg3x
- y=ln⁴(1-arctg3x)
- y=ln^41-arctg3x
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Expresiones semejantes
- y=ln^4(1+arctg3x)
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Expresiones con funciones
- ln
- ln(x+3)^3
- ln((x^2)/(1-x^2))
- ln(x^2-2x)
- ln(e)
- ln(x-3)
Derivada de y=ln^4(1-arctg3x)
Solución
Ha introducido
[src]
4 log (1 - atan(3*x))
$$\log{\left(1 - \operatorname{atan}{\left(3 x \right)} \right)}^{4}$$
log(1 - atan(3*x))^4
Primera derivada
[src]
3
-12*log (1 - atan(3*x))
--------------------------
/ 2\
(1 - atan(3*x))*\1 + 9*x /
$$- \frac{12 \log{\left(1 - \operatorname{atan}{\left(3 x \right)} \right)}^{3}}{\left(1 - \operatorname{atan}{\left(3 x \right)}\right) \left(9 x^{2} + 1\right)}$$
Segunda derivada
[src]
2 / 3 log(1 - atan(3*x)) \
36*log (1 - atan(3*x))*|-------------- - ------------------ - 6*x*log(1 - atan(3*x))|
\-1 + atan(3*x) -1 + atan(3*x) /
-------------------------------------------------------------------------------------
2
/ 2\
\1 + 9*x / *(-1 + atan(3*x))
$$\frac{36 \left(- 6 x \log{\left(1 - \operatorname{atan}{\left(3 x \right)} \right)} - \frac{\log{\left(1 - \operatorname{atan}{\left(3 x \right)} \right)}}{\operatorname{atan}{\left(3 x \right)} - 1} + \frac{3}{\operatorname{atan}{\left(3 x \right)} - 1}\right) \log{\left(1 - \operatorname{atan}{\left(3 x \right)} \right)}^{2}}{\left(9 x^{2} + 1\right)^{2} \left(\operatorname{atan}{\left(3 x \right)} - 1\right)}$$
Tercera derivada
[src]
/ 2 2 2 2 \
| 2 6 9*log(1 - atan(3*x)) 2*log (1 - atan(3*x)) 72*x *log (1 - atan(3*x)) 54*x*log(1 - atan(3*x)) 18*x*log (1 - atan(3*x)) |
108*|- 2*log (1 - atan(3*x)) + ---------------------------- - ---------------------------- + ---------------------------- + ------------------------- - --------------------------- + ---------------------------|*log(1 - atan(3*x))
| / 2\ 2 / 2\ 2 / 2\ 2 2 / 2\ / 2\ |
\ \1 + 9*x /*(-1 + atan(3*x)) \1 + 9*x /*(-1 + atan(3*x)) \1 + 9*x /*(-1 + atan(3*x)) 1 + 9*x \1 + 9*x /*(-1 + atan(3*x)) \1 + 9*x /*(-1 + atan(3*x))/
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
2
/ 2\
\1 + 9*x / *(-1 + atan(3*x))
$$\frac{108 \left(\frac{72 x^{2} \log{\left(1 - \operatorname{atan}{\left(3 x \right)} \right)}^{2}}{9 x^{2} + 1} + \frac{18 x \log{\left(1 - \operatorname{atan}{\left(3 x \right)} \right)}^{2}}{\left(9 x^{2} + 1\right) \left(\operatorname{atan}{\left(3 x \right)} - 1\right)} - \frac{54 x \log{\left(1 - \operatorname{atan}{\left(3 x \right)} \right)}}{\left(9 x^{2} + 1\right) \left(\operatorname{atan}{\left(3 x \right)} - 1\right)} - 2 \log{\left(1 - \operatorname{atan}{\left(3 x \right)} \right)}^{2} + \frac{2 \log{\left(1 - \operatorname{atan}{\left(3 x \right)} \right)}^{2}}{\left(9 x^{2} + 1\right) \left(\operatorname{atan}{\left(3 x \right)} - 1\right)^{2}} - \frac{9 \log{\left(1 - \operatorname{atan}{\left(3 x \right)} \right)}}{\left(9 x^{2} + 1\right) \left(\operatorname{atan}{\left(3 x \right)} - 1\right)^{2}} + \frac{6}{\left(9 x^{2} + 1\right) \left(\operatorname{atan}{\left(3 x \right)} - 1\right)^{2}}\right) \log{\left(1 - \operatorname{atan}{\left(3 x \right)} \right)}}{\left(9 x^{2} + 1\right)^{2} \left(\operatorname{atan}{\left(3 x \right)} - 1\right)}$$
Gráfico