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:
-
Derivada de x^-(4/5)
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Derivada de x^-8
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Derivada de x^2/lnx
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Derivada de √x+2
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Expresiones idénticas
- y=ln^ tres (uno +arctg5x)
- y es igual a ln al cubo (1 más arctg5x)
- y es igual a ln en el grado tres (uno más arctg5x)
- y=ln3(1+arctg5x)
- y=ln31+arctg5x
- y=ln³(1+arctg5x)
- y=ln en el grado 3(1+arctg5x)
- y=ln^31+arctg5x
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Expresiones semejantes
- y=ln^3(1-arctg5x)
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Expresiones con funciones
- ln
- ln(x/5)
- ln(e^(2*x)+1)
- ln(x^2+2)
- ln(1+x²)
- ln√x-2
Derivada de y=ln^3(1+arctg5x)
Solución
Ha introducido
[src]
3 log (1 + atan(5*x))
$$\log{\left(\operatorname{atan}{\left(5 x \right)} + 1 \right)}^{3}$$
log(1 + atan(5*x))^3
Primera derivada
[src]
2 15*log (1 + atan(5*x)) --------------------------- / 2\ \1 + 25*x /*(1 + atan(5*x))
$$\frac{15 \log{\left(\operatorname{atan}{\left(5 x \right)} + 1 \right)}^{2}}{\left(25 x^{2} + 1\right) \left(\operatorname{atan}{\left(5 x \right)} + 1\right)}$$
Segunda derivada
[src]
/ 2 log(1 + atan(5*x)) \
75*|------------- - ------------------ - 10*x*log(1 + atan(5*x))|*log(1 + atan(5*x))
\1 + atan(5*x) 1 + atan(5*x) /
------------------------------------------------------------------------------------
2
/ 2\
\1 + 25*x / *(1 + atan(5*x))
$$\frac{75 \left(- 10 x \log{\left(\operatorname{atan}{\left(5 x \right)} + 1 \right)} - \frac{\log{\left(\operatorname{atan}{\left(5 x \right)} + 1 \right)}}{\operatorname{atan}{\left(5 x \right)} + 1} + \frac{2}{\operatorname{atan}{\left(5 x \right)} + 1}\right) \log{\left(\operatorname{atan}{\left(5 x \right)} + 1 \right)}}{\left(25 x^{2} + 1\right)^{2} \left(\operatorname{atan}{\left(5 x \right)} + 1\right)}$$
Tercera derivada
[src]
/ 2 2 2 2 \
| 2 1 log (1 + atan(5*x)) 3*log(1 + atan(5*x)) 100*x *log (1 + atan(5*x)) 30*x*log(1 + atan(5*x)) 15*x*log (1 + atan(5*x)) |
750*|- log (1 + atan(5*x)) + ---------------------------- + ---------------------------- - ---------------------------- + -------------------------- - --------------------------- + ---------------------------|
| / 2\ 2 / 2\ 2 / 2\ 2 2 / 2\ / 2\ |
\ \1 + 25*x /*(1 + atan(5*x)) \1 + 25*x /*(1 + atan(5*x)) \1 + 25*x /*(1 + atan(5*x)) 1 + 25*x \1 + 25*x /*(1 + atan(5*x)) \1 + 25*x /*(1 + atan(5*x))/
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
2
/ 2\
\1 + 25*x / *(1 + atan(5*x))
$$\frac{750 \left(\frac{100 x^{2} \log{\left(\operatorname{atan}{\left(5 x \right)} + 1 \right)}^{2}}{25 x^{2} + 1} + \frac{15 x \log{\left(\operatorname{atan}{\left(5 x \right)} + 1 \right)}^{2}}{\left(25 x^{2} + 1\right) \left(\operatorname{atan}{\left(5 x \right)} + 1\right)} - \frac{30 x \log{\left(\operatorname{atan}{\left(5 x \right)} + 1 \right)}}{\left(25 x^{2} + 1\right) \left(\operatorname{atan}{\left(5 x \right)} + 1\right)} - \log{\left(\operatorname{atan}{\left(5 x \right)} + 1 \right)}^{2} + \frac{\log{\left(\operatorname{atan}{\left(5 x \right)} + 1 \right)}^{2}}{\left(25 x^{2} + 1\right) \left(\operatorname{atan}{\left(5 x \right)} + 1\right)^{2}} - \frac{3 \log{\left(\operatorname{atan}{\left(5 x \right)} + 1 \right)}}{\left(25 x^{2} + 1\right) \left(\operatorname{atan}{\left(5 x \right)} + 1\right)^{2}} + \frac{1}{\left(25 x^{2} + 1\right) \left(\operatorname{atan}{\left(5 x \right)} + 1\right)^{2}}\right)}{\left(25 x^{2} + 1\right)^{2} \left(\operatorname{atan}{\left(5 x \right)} + 1\right)}$$