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 (-4)/x^2
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Derivada de 2/x²
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Derivada de -2*y
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Derivada de (3+2x)/(x-5)
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Expresiones idénticas
- y=arcctg^ tres (2x)*ln^ cinco (x)
- y es igual a arcctg al cubo (2x) multiplicar por ln en el grado 5(x)
- y es igual a arcctg en el grado tres (2x) multiplicar por ln en el grado cinco (x)
- y=arcctg3(2x)*ln5(x)
- y=arcctg32x*ln5x
- y=arcctg³(2x)*ln⁵(x)
- y=arcctg en el grado 3(2x)*ln en el grado 5(x)
- y=arcctg^3(2x)ln^5(x)
- y=arcctg3(2x)ln5(x)
- y=arcctg32xln5x
- y=arcctg^32xln^5x
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Expresiones con funciones
- ln
- ln(×)
- ln(x+a)
- ln(e^x-e^a)
- ln^3(3x)
- ln(2/x)
Derivada de y=arcctg^3(2x)*ln^5(x)
Solución
Ha introducido
[src]
3 5 acot (2*x)*log (x)
$$\log{\left(x \right)}^{5} \operatorname{acot}^{3}{\left(2 x \right)}$$
acot(2*x)^3*log(x)^5
Primera derivada
[src]
2 5 3 4
6*acot (2*x)*log (x) 5*acot (2*x)*log (x)
- -------------------- + --------------------
2 x
1 + 4*x
$$- \frac{6 \log{\left(x \right)}^{5} \operatorname{acot}^{2}{\left(2 x \right)}}{4 x^{2} + 1} + \frac{5 \log{\left(x \right)}^{4} \operatorname{acot}^{3}{\left(2 x \right)}}{x}$$
Segunda derivada
[src]
/ 2 2 \
3 | 5*acot (2*x)*(-4 + log(x)) 24*log (x)*(1 + 2*x*acot(2*x)) 60*acot(2*x)*log(x)|
log (x)*|- -------------------------- + ------------------------------ - -------------------|*acot(2*x)
| 2 2 / 2\ |
| x / 2\ x*\1 + 4*x / |
\ \1 + 4*x / /
$$\left(\frac{24 \left(2 x \operatorname{acot}{\left(2 x \right)} + 1\right) \log{\left(x \right)}^{2}}{\left(4 x^{2} + 1\right)^{2}} - \frac{60 \log{\left(x \right)} \operatorname{acot}{\left(2 x \right)}}{x \left(4 x^{2} + 1\right)} - \frac{5 \left(\log{\left(x \right)} - 4\right) \operatorname{acot}^{2}{\left(2 x \right)}}{x^{2}}\right) \log{\left(x \right)}^{3} \operatorname{acot}{\left(2 x \right)}$$
Tercera derivada
[src]
/ / 2 2 \ \
| 3 | 1 2 12*x*acot(2*x) 16*x *acot (2*x)| |
| 24*log (x)*|-------- - acot (2*x) + -------------- + ----------------| |
| | 2 2 2 | 3 / 2 \ 2 2 |
2 | \1 + 4*x 1 + 4*x 1 + 4*x / 5*acot (2*x)*\6 + log (x) - 6*log(x)/ 45*acot (2*x)*(-4 + log(x))*log(x) 180*log (x)*(1 + 2*x*acot(2*x))*acot(2*x)|
2*log (x)*|- ---------------------------------------------------------------------- + ------------------------------------- + ---------------------------------- + -----------------------------------------|
| 2 3 2 / 2\ 2 |
| / 2\ x x *\1 + 4*x / / 2\ |
\ \1 + 4*x / x*\1 + 4*x / /
$$2 \left(- \frac{24 \left(\frac{16 x^{2} \operatorname{acot}^{2}{\left(2 x \right)}}{4 x^{2} + 1} + \frac{12 x \operatorname{acot}{\left(2 x \right)}}{4 x^{2} + 1} - \operatorname{acot}^{2}{\left(2 x \right)} + \frac{1}{4 x^{2} + 1}\right) \log{\left(x \right)}^{3}}{\left(4 x^{2} + 1\right)^{2}} + \frac{180 \left(2 x \operatorname{acot}{\left(2 x \right)} + 1\right) \log{\left(x \right)}^{2} \operatorname{acot}{\left(2 x \right)}}{x \left(4 x^{2} + 1\right)^{2}} + \frac{45 \left(\log{\left(x \right)} - 4\right) \log{\left(x \right)} \operatorname{acot}^{2}{\left(2 x \right)}}{x^{2} \left(4 x^{2} + 1\right)} + \frac{5 \left(\log{\left(x \right)}^{2} - 6 \log{\left(x \right)} + 6\right) \operatorname{acot}^{3}{\left(2 x \right)}}{x^{3}}\right) \log{\left(x \right)}^{2}$$
Gráfico