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^-(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^5x×arcctg^ dos (3x+ uno)
- y es igual a ln en el grado 5x×arcctg al cuadrado (3x más 1)
- y es igual a ln en el grado 5x×arcctg en el grado dos (3x más uno)
- y=ln5x×arcctg2(3x+1)
- y=ln5x×arcctg23x+1
- y=ln⁵x×arcctg²(3x+1)
- y=ln en el grado 5x×arcctg en el grado 2(3x+1)
- y=ln^5x×arcctg^23x+1
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Expresiones semejantes
- y=ln^5x×arcctg^2(3x-1)
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Expresiones con funciones
- ln
- ln(x/5)
- ln(e^(2*x)+1)
- ln(x+sqrt(a^2+x^2))
- ln(x+8)
- ln(x+1)²
Derivada de y=ln^5x×arcctg^2(3x+1)
Solución
Ha introducido
[src]
5 2 log (x)*acot (3*x + 1)
$$\log{\left(x \right)}^{5} \operatorname{acot}^{2}{\left(3 x + 1 \right)}$$
log(x)^5*acot(3*x + 1)^2
Primera derivada
[src]
5 2 4
6*log (x)*acot(3*x + 1) 5*acot (3*x + 1)*log (x)
- ----------------------- + ------------------------
2 x
1 + (3*x + 1)
$$- \frac{6 \log{\left(x \right)}^{5} \operatorname{acot}{\left(3 x + 1 \right)}}{\left(3 x + 1\right)^{2} + 1} + \frac{5 \log{\left(x \right)}^{4} \operatorname{acot}^{2}{\left(3 x + 1 \right)}}{x}$$
Segunda derivada
[src]
/ 2 2 \
3 | 5*acot (1 + 3*x)*(-4 + log(x)) 18*log (x)*(1 + 2*(1 + 3*x)*acot(1 + 3*x)) 60*acot(1 + 3*x)*log(x)|
log (x)*|- ------------------------------ + ------------------------------------------ - -----------------------|
| 2 2 / 2\ |
| x / 2\ x*\1 + (1 + 3*x) / |
\ \1 + (1 + 3*x) / /
$$\left(\frac{18 \left(2 \left(3 x + 1\right) \operatorname{acot}{\left(3 x + 1 \right)} + 1\right) \log{\left(x \right)}^{2}}{\left(\left(3 x + 1\right)^{2} + 1\right)^{2}} - \frac{60 \log{\left(x \right)} \operatorname{acot}{\left(3 x + 1 \right)}}{x \left(\left(3 x + 1\right)^{2} + 1\right)} - \frac{5 \left(\log{\left(x \right)} - 4\right) \operatorname{acot}^{2}{\left(3 x + 1 \right)}}{x^{2}}\right) \log{\left(x \right)}^{3}$$
Tercera derivada
[src]
/ / 2 \ \
| 3 | 3*(1 + 3*x) 4*(1 + 3*x) *acot(1 + 3*x)| |
| 54*log (x)*|-acot(1 + 3*x) + -------------- + --------------------------| |
| | 2 2 | 2 / 2 \ 2 |
2 | \ 1 + (1 + 3*x) 1 + (1 + 3*x) / 5*acot (1 + 3*x)*\6 + log (x) - 6*log(x)/ 135*log (x)*(1 + 2*(1 + 3*x)*acot(1 + 3*x)) 45*(-4 + log(x))*acot(1 + 3*x)*log(x)|
2*log (x)*|- ------------------------------------------------------------------------- + ----------------------------------------- + ------------------------------------------- + -------------------------------------|
| 2 3 2 2 / 2\ |
| / 2\ x / 2\ x *\1 + (1 + 3*x) / |
\ \1 + (1 + 3*x) / x*\1 + (1 + 3*x) / /
$$2 \left(- \frac{54 \left(\frac{4 \left(3 x + 1\right)^{2} \operatorname{acot}{\left(3 x + 1 \right)}}{\left(3 x + 1\right)^{2} + 1} + \frac{3 \left(3 x + 1\right)}{\left(3 x + 1\right)^{2} + 1} - \operatorname{acot}{\left(3 x + 1 \right)}\right) \log{\left(x \right)}^{3}}{\left(\left(3 x + 1\right)^{2} + 1\right)^{2}} + \frac{135 \left(2 \left(3 x + 1\right) \operatorname{acot}{\left(3 x + 1 \right)} + 1\right) \log{\left(x \right)}^{2}}{x \left(\left(3 x + 1\right)^{2} + 1\right)^{2}} + \frac{45 \left(\log{\left(x \right)} - 4\right) \log{\left(x \right)} \operatorname{acot}{\left(3 x + 1 \right)}}{x^{2} \left(\left(3 x + 1\right)^{2} + 1\right)} + \frac{5 \left(\log{\left(x \right)}^{2} - 6 \log{\left(x \right)} + 6\right) \operatorname{acot}^{2}{\left(3 x + 1 \right)}}{x^{3}}\right) \log{\left(x \right)}^{2}$$
Gráfico