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^-7
- Derivada de i*n*x
-
Derivada de 5*tan(x)^3+sin(4*x)*e^((-x)/7)
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Derivada de y=-6/x
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Expresiones idénticas
- y=arcctg^32x*ln^5x
- y es igual a arcctg al cubo 2x multiplicar por ln en el grado 5x
- y=arcctg32x*ln5x
- y=arcctg³2x*ln⁵x
- y=arcctg en el grado 32x*ln en el grado 5x
- y=arcctg^32xln^5x
- y=arcctg32xln5x
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Expresiones con funciones
- ln
- ln(e^(2*x)+1)
- ln(ax)
- ln(x+sqrt(a^2+x^2))
- ln(3x²)
- ln(x+8)
Derivada de y=arcctg^32x*ln^5x
Solución
Ha introducido
[src]
32 5 acot (x)*log (x)
$$\log{\left(x \right)}^{5} \operatorname{acot}^{32}{\left(x \right)}$$
acot(x)^32*log(x)^5
Primera derivada
[src]
31 5 32 4
32*acot (x)*log (x) 5*acot (x)*log (x)
- -------------------- + -------------------
2 x
1 + x
$$- \frac{32 \log{\left(x \right)}^{5} \operatorname{acot}^{31}{\left(x \right)}}{x^{2} + 1} + \frac{5 \log{\left(x \right)}^{4} \operatorname{acot}^{32}{\left(x \right)}}{x}$$
Segunda derivada
[src]
/ 2 2 \
30 3 | 5*acot (x)*(-4 + log(x)) 32*log (x)*(31 + 2*x*acot(x)) 320*acot(x)*log(x)|
acot (x)*log (x)*|- ------------------------ + ----------------------------- - ------------------|
| 2 2 / 2\ |
| x / 2\ x*\1 + x / |
\ \1 + x / /
$$\left(\frac{32 \left(2 x \operatorname{acot}{\left(x \right)} + 31\right) \log{\left(x \right)}^{2}}{\left(x^{2} + 1\right)^{2}} - \frac{320 \log{\left(x \right)} \operatorname{acot}{\left(x \right)}}{x \left(x^{2} + 1\right)} - \frac{5 \left(\log{\left(x \right)} - 4\right) \operatorname{acot}^{2}{\left(x \right)}}{x^{2}}\right) \log{\left(x \right)}^{3} \operatorname{acot}^{30}{\left(x \right)}$$
Tercera derivada
[src]
/ / 2 2 \ \
| 3 | 2 465 4*x *acot (x) 93*x*acot(x)| |
| 32*log (x)*|- acot (x) + ------ + ------------- + ------------| |
| | 2 2 2 | 3 / 2 \ 2 2 |
29 2 | \ 1 + x 1 + x 1 + x / 5*acot (x)*\6 + log (x) - 6*log(x)/ 240*log (x)*(31 + 2*x*acot(x))*acot(x) 240*acot (x)*(-4 + log(x))*log(x)|
2*acot (x)*log (x)*|- --------------------------------------------------------------- + ----------------------------------- + -------------------------------------- + ---------------------------------|
| 2 3 2 2 / 2\ |
| / 2\ x / 2\ x *\1 + x / |
\ \1 + x / x*\1 + x / /
$$2 \left(- \frac{32 \left(\frac{4 x^{2} \operatorname{acot}^{2}{\left(x \right)}}{x^{2} + 1} + \frac{93 x \operatorname{acot}{\left(x \right)}}{x^{2} + 1} - \operatorname{acot}^{2}{\left(x \right)} + \frac{465}{x^{2} + 1}\right) \log{\left(x \right)}^{3}}{\left(x^{2} + 1\right)^{2}} + \frac{240 \left(2 x \operatorname{acot}{\left(x \right)} + 31\right) \log{\left(x \right)}^{2} \operatorname{acot}{\left(x \right)}}{x \left(x^{2} + 1\right)^{2}} + \frac{240 \left(\log{\left(x \right)} - 4\right) \log{\left(x \right)} \operatorname{acot}^{2}{\left(x \right)}}{x^{2} \left(x^{2} + 1\right)} + \frac{5 \left(\log{\left(x \right)}^{2} - 6 \log{\left(x \right)} + 6\right) \operatorname{acot}^{3}{\left(x \right)}}{x^{3}}\right) \log{\left(x \right)}^{2} \operatorname{acot}^{29}{\left(x \right)}$$
Gráfico