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 1/(x+3)
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Derivada de 2^(5*x)
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Derivada de x^(5*x)
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Derivada de x^(7/5)
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Expresiones idénticas
- y=arctg^ tres (lnx^ uno / dos /x+ dos)
- y es igual a arctg al cubo (lnx en el grado 1 dividir por 2 dividir por x más 2)
- y es igual a arctg en el grado tres (lnx en el grado uno dividir por dos dividir por x más dos)
- y=arctg3(lnx1/2/x+2)
- y=arctg3lnx1/2/x+2
- y=arctg³(lnx^1/2/x+2)
- y=arctg en el grado 3(lnx en el grado 1/2/x+2)
- y=arctg^3lnx^1/2/x+2
- y=arctg^3(lnx^1 dividir por 2 dividir por x+2)
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Expresiones semejantes
- y=arctg^3(lnx^1/2/x-2)
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Expresiones con funciones
- arctg
- arctg^2(1/x)
- arctg(x+cosx)
Derivada de y=arctg^3(lnx^1/2/x+2)
Solución
Ha introducido
[src]
/ ________ \
3|\/ log(x) |
atan |---------- + 2|
\ x /
$$\operatorname{atan}^{3}{\left(2 + \frac{\sqrt{\log{\left(x \right)}}}{x} \right)}$$
atan(sqrt(log(x))/x + 2)^3
Primera derivada
[src]
/ ________ \ / ________\
2|\/ log(x) | | 1 \/ log(x) |
3*atan |---------- + 2|*|--------------- - ----------|
\ x / | 2 ________ 2 |
\2*x *\/ log(x) x /
------------------------------------------------------
2
/ ________ \
|\/ log(x) |
1 + |---------- + 2|
\ x /
$$\frac{3 \left(- \frac{\sqrt{\log{\left(x \right)}}}{x^{2}} + \frac{1}{2 x^{2} \sqrt{\log{\left(x \right)}}}\right) \operatorname{atan}^{2}{\left(2 + \frac{\sqrt{\log{\left(x \right)}}}{x} \right)}}{\left(2 + \frac{\sqrt{\log{\left(x \right)}}}{x}\right)^{2} + 1}$$
Segunda derivada
[src]
/ 2 2 / ________\ / ________\\
| / 1 ________\ / 1 ________\ | \/ log(x) | | \/ log(x) ||
| 2*|- ---------- + 2*\/ log(x) | 2*|- ---------- + 2*\/ log(x) | *|2 + ----------|*atan|2 + ----------||
| / ________\ | ________ | | ________ | \ x / \ x /| / ________\
| / 1 ________ 6 \ | \/ log(x) | \ \/ log(x) / \ \/ log(x) / | | \/ log(x) |
3*|- |--------- - 8*\/ log(x) + ----------|*atan|2 + ----------| + -------------------------------- - ----------------------------------------------------------------------|*atan|2 + ----------|
| | 3/2 ________| \ x / / 2\ / 2\ | \ x /
| \log (x) \/ log(x) / | / ________\ | | / ________\ | |
| | | \/ log(x) | | | | \/ log(x) | | |
| x*|1 + |2 + ----------| | x*|1 + |2 + ----------| | |
\ \ \ x / / \ \ x / / /
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
/ 2\
| / ________\ |
3 | | \/ log(x) | |
4*x *|1 + |2 + ----------| |
\ \ x / /
$$\frac{3 \left(- \left(- 8 \sqrt{\log{\left(x \right)}} + \frac{6}{\sqrt{\log{\left(x \right)}}} + \frac{1}{\log{\left(x \right)}^{\frac{3}{2}}}\right) \operatorname{atan}{\left(2 + \frac{\sqrt{\log{\left(x \right)}}}{x} \right)} - \frac{2 \left(2 + \frac{\sqrt{\log{\left(x \right)}}}{x}\right) \left(2 \sqrt{\log{\left(x \right)}} - \frac{1}{\sqrt{\log{\left(x \right)}}}\right)^{2} \operatorname{atan}{\left(2 + \frac{\sqrt{\log{\left(x \right)}}}{x} \right)}}{x \left(\left(2 + \frac{\sqrt{\log{\left(x \right)}}}{x}\right)^{2} + 1\right)} + \frac{2 \left(2 \sqrt{\log{\left(x \right)}} - \frac{1}{\sqrt{\log{\left(x \right)}}}\right)^{2}}{x \left(\left(2 + \frac{\sqrt{\log{\left(x \right)}}}{x}\right)^{2} + 1\right)}\right) \operatorname{atan}{\left(2 + \frac{\sqrt{\log{\left(x \right)}}}{x} \right)}}{4 x^{3} \left(\left(2 + \frac{\sqrt{\log{\left(x \right)}}}{x}\right)^{2} + 1\right)}$$
Tercera derivada
[src]
/ 2 \
| / ________\ 3 3 / ________\ / ________\ 3 / ________\ 3 / ________\ / ________\ / ________\ / ________\ / ________\ |
| 2| \/ log(x) | / ________ 3 12 44 \ / 1 ________\ / 1 ________\ 2| \/ log(x) | | \/ log(x) | / 1 ________\ 2| \/ log(x) | / 1 ________\ | \/ log(x) | | \/ log(x) | / 1 ________\ / 1 ________ 6 \ | \/ log(x) | 2| \/ log(x) | | \/ log(x) | / 1 ________\ / 1 ________ 6 \|
|atan |2 + ----------|*|- 48*\/ log(x) + --------- + --------- + ----------| |- ---------- + 2*\/ log(x) | |- ---------- + 2*\/ log(x) | *atan |2 + ----------| |2 + ----------| *|- ---------- + 2*\/ log(x) | *atan |2 + ----------| 3*|- ---------- + 2*\/ log(x) | *|2 + ----------|*atan|2 + ----------| 3*|- ---------- + 2*\/ log(x) |*|--------- - 8*\/ log(x) + ----------|*atan|2 + ----------| 3*atan |2 + ----------|*|2 + ----------|*|- ---------- + 2*\/ log(x) |*|--------- - 8*\/ log(x) + ----------||
| \ x / | 5/2 3/2 ________| | ________ | | ________ | \ x / \ x / | ________ | \ x / | ________ | \ x / \ x / | ________ | | 3/2 ________| \ x / \ x / \ x / | ________ | | 3/2 ________||
| \ log (x) log (x) \/ log(x) / \ \/ log(x) / \ \/ log(x) / \ \/ log(x) / \ \/ log(x) / \ \/ log(x) / \log (x) \/ log(x) / \ \/ log(x) / \log (x) \/ log(x) /|
3*|---------------------------------------------------------------------------- - ------------------------------ + ---------------------------------------------------- - ---------------------------------------------------------------------- + ---------------------------------------------------------------------- + -------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------|
| 8 2 / 2\ 2 2 / 2\ / 2\ |
| / 2\ | / ________\ | / 2\ / 2\ | / ________\ | | / ________\ | |
| | / ________\ | 2 | | \/ log(x) | | | / ________\ | | / ________\ | | | \/ log(x) | | | | \/ log(x) | | |
| 2 | | \/ log(x) | | 4*x *|1 + |2 + ----------| | 2 | | \/ log(x) | | 2 | | \/ log(x) | | 4*x*|1 + |2 + ----------| | 4*x*|1 + |2 + ----------| | |
| 4*x *|1 + |2 + ----------| | \ \ x / / x *|1 + |2 + ----------| | 2*x *|1 + |2 + ----------| | \ \ x / / \ \ x / / |
\ \ \ x / / \ \ x / / \ \ x / / /
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
/ 2\
| / ________\ |
4 | | \/ log(x) | |
x *|1 + |2 + ----------| |
\ \ x / /
$$\frac{3 \left(\frac{\left(- 48 \sqrt{\log{\left(x \right)}} + \frac{44}{\sqrt{\log{\left(x \right)}}} + \frac{12}{\log{\left(x \right)}^{\frac{3}{2}}} + \frac{3}{\log{\left(x \right)}^{\frac{5}{2}}}\right) \operatorname{atan}^{2}{\left(2 + \frac{\sqrt{\log{\left(x \right)}}}{x} \right)}}{8} - \frac{3 \left(2 + \frac{\sqrt{\log{\left(x \right)}}}{x}\right) \left(2 \sqrt{\log{\left(x \right)}} - \frac{1}{\sqrt{\log{\left(x \right)}}}\right) \left(- 8 \sqrt{\log{\left(x \right)}} + \frac{6}{\sqrt{\log{\left(x \right)}}} + \frac{1}{\log{\left(x \right)}^{\frac{3}{2}}}\right) \operatorname{atan}^{2}{\left(2 + \frac{\sqrt{\log{\left(x \right)}}}{x} \right)}}{4 x \left(\left(2 + \frac{\sqrt{\log{\left(x \right)}}}{x}\right)^{2} + 1\right)} + \frac{3 \left(2 \sqrt{\log{\left(x \right)}} - \frac{1}{\sqrt{\log{\left(x \right)}}}\right) \left(- 8 \sqrt{\log{\left(x \right)}} + \frac{6}{\sqrt{\log{\left(x \right)}}} + \frac{1}{\log{\left(x \right)}^{\frac{3}{2}}}\right) \operatorname{atan}{\left(2 + \frac{\sqrt{\log{\left(x \right)}}}{x} \right)}}{4 x \left(\left(2 + \frac{\sqrt{\log{\left(x \right)}}}{x}\right)^{2} + 1\right)} - \frac{\left(2 + \frac{\sqrt{\log{\left(x \right)}}}{x}\right)^{2} \left(2 \sqrt{\log{\left(x \right)}} - \frac{1}{\sqrt{\log{\left(x \right)}}}\right)^{3} \operatorname{atan}^{2}{\left(2 + \frac{\sqrt{\log{\left(x \right)}}}{x} \right)}}{x^{2} \left(\left(2 + \frac{\sqrt{\log{\left(x \right)}}}{x}\right)^{2} + 1\right)^{2}} + \frac{3 \left(2 + \frac{\sqrt{\log{\left(x \right)}}}{x}\right) \left(2 \sqrt{\log{\left(x \right)}} - \frac{1}{\sqrt{\log{\left(x \right)}}}\right)^{3} \operatorname{atan}{\left(2 + \frac{\sqrt{\log{\left(x \right)}}}{x} \right)}}{2 x^{2} \left(\left(2 + \frac{\sqrt{\log{\left(x \right)}}}{x}\right)^{2} + 1\right)^{2}} + \frac{\left(2 \sqrt{\log{\left(x \right)}} - \frac{1}{\sqrt{\log{\left(x \right)}}}\right)^{3} \operatorname{atan}^{2}{\left(2 + \frac{\sqrt{\log{\left(x \right)}}}{x} \right)}}{4 x^{2} \left(\left(2 + \frac{\sqrt{\log{\left(x \right)}}}{x}\right)^{2} + 1\right)} - \frac{\left(2 \sqrt{\log{\left(x \right)}} - \frac{1}{\sqrt{\log{\left(x \right)}}}\right)^{3}}{4 x^{2} \left(\left(2 + \frac{\sqrt{\log{\left(x \right)}}}{x}\right)^{2} + 1\right)^{2}}\right)}{x^{4} \left(\left(2 + \frac{\sqrt{\log{\left(x \right)}}}{x}\right)^{2} + 1\right)}$$
Gráfico