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 v
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Derivada de (x+12)e^(12-x)
- Derivada de u/v
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Derivada de x^(1/10)
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Expresiones idénticas
- y=arctg^ tres (ln(x^ uno / dos)/(x+ dos))
- y es igual a arctg al cubo (ln(x en el grado 1 dividir por 2) dividir por (x más 2))
- y es igual a arctg en el grado tres (ln(x en el grado uno dividir por dos) dividir por (x más dos))
- y=arctg3(ln(x1/2)/(x+2))
- y=arctg3lnx1/2/x+2
- y=arctg³(ln(x^1/2)/(x+2))
- y=arctg en el grado 3(ln(x en el grado 1/2)/(x+2))
- y=arctg^3lnx^1/2/x+2
- y=arctg^3(ln(x^1 dividir por 2) dividir por (x+2))
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Expresiones semejantes
- y=arctg^3(ln(x^1/2)/(x-2))
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Expresiones con funciones
- ln
- ln(1+e^-x)
- ln2*((((1+cos(2*x))^3)^(1/2)))
- ln((x+a)^0.5)
Derivada de y=arctg^3(ln(x^1/2)/(x+2))
Solución
Ha introducido
[src]
/ / ___\\
3|log\\/ x /|
atan |----------|
\ x + 2 /
$$\operatorname{atan}^{3}{\left(\frac{\log{\left(\sqrt{x} \right)}}{x + 2} \right)}$$
atan(log(sqrt(x))/(x + 2))^3
Primera derivada
[src]
/ / ___\\ / / ___\\
2|log\\/ x /| | 1 log\\/ x /|
3*atan |----------|*|----------- - ----------|
\ x + 2 / |2*x*(x + 2) 2 |
\ (x + 2) /
----------------------------------------------
2/ ___\
log \\/ x /
1 + -----------
2
(x + 2)
$$\frac{3 \left(- \frac{\log{\left(\sqrt{x} \right)}}{\left(x + 2\right)^{2}} + \frac{1}{2 x \left(x + 2\right)}\right) \operatorname{atan}^{2}{\left(\frac{\log{\left(\sqrt{x} \right)}}{x + 2} \right)}}{1 + \frac{\log{\left(\sqrt{x} \right)}^{2}}{\left(x + 2\right)^{2}}}$$
Segunda derivada
[src]
/ 2 2 \
| / / ___\\ / / ___\\ / / ___\\ |
| | 1 2*log\\/ x /| | 1 2*log\\/ x /| |log\\/ x /| / ___\|
| / / ___\ \ / / ___\\ |- - + ------------| |- - + ------------| *atan|----------|*log\\/ x /| / / ___\\
| |1 4*log\\/ x / 2 | |log\\/ x /| \ x 2 + x / \ x 2 + x / \ 2 + x / | |log\\/ x /|
3*|- |-- - ------------ + ---------|*atan|----------| + ------------------------- - -------------------------------------------------|*atan|----------|
| | 2 2 x*(2 + x)| \ 2 + x / / 2/ ___\\ / 2/ ___\\ | \ 2 + x /
| \x (2 + x) / | log \\/ x /| | log \\/ x /| 2 |
| |1 + -----------|*(2 + x) |1 + -----------|*(2 + x) |
| | 2 | | 2 | |
\ \ (2 + x) / \ (2 + x) / /
-------------------------------------------------------------------------------------------------------------------------------------------------------
/ 2/ ___\\
| log \\/ x /|
2*|1 + -----------|*(2 + x)
| 2 |
\ (2 + x) /
$$\frac{3 \left(- \left(- \frac{4 \log{\left(\sqrt{x} \right)}}{\left(x + 2\right)^{2}} + \frac{2}{x \left(x + 2\right)} + \frac{1}{x^{2}}\right) \operatorname{atan}{\left(\frac{\log{\left(\sqrt{x} \right)}}{x + 2} \right)} + \frac{\left(\frac{2 \log{\left(\sqrt{x} \right)}}{x + 2} - \frac{1}{x}\right)^{2}}{\left(1 + \frac{\log{\left(\sqrt{x} \right)}^{2}}{\left(x + 2\right)^{2}}\right) \left(x + 2\right)} - \frac{\left(\frac{2 \log{\left(\sqrt{x} \right)}}{x + 2} - \frac{1}{x}\right)^{2} \log{\left(\sqrt{x} \right)} \operatorname{atan}{\left(\frac{\log{\left(\sqrt{x} \right)}}{x + 2} \right)}}{\left(1 + \frac{\log{\left(\sqrt{x} \right)}^{2}}{\left(x + 2\right)^{2}}\right) \left(x + 2\right)^{2}}\right) \operatorname{atan}{\left(\frac{\log{\left(\sqrt{x} \right)}}{x + 2} \right)}}{2 \left(1 + \frac{\log{\left(\sqrt{x} \right)}^{2}}{\left(x + 2\right)^{2}}\right) \left(x + 2\right)}$$
Tercera derivada
[src]
/ / / ___\\ / / ___\ \ 3 3 / / ___\\ / / ___\\ / / ___\ 2/ ___\ / ___\\ / / ___\\ / / ___\ \ / / ___\\ 3 / / ___\\ / / ___\\ / / ___\ \ \
| 2|log\\/ x /| |2 12*log\\/ x / 3 6 | / / ___\\ / / ___\\ / / ___\\ 2|log\\/ x /| | 1 2*log\\/ x /| |1 2*log\\/ x / 12*log \\/ x / 8*log\\/ x /| | 1 2*log\\/ x /| |1 4*log\\/ x / 2 | |log\\/ x /| / / ___\\ / / ___\\ 2|log\\/ x /| | 1 2*log\\/ x /| |1 4*log\\/ x / 2 | / ___\|
|atan |----------|*|-- - ------------- + ---------- + ----------| | 1 2*log\\/ x /| | 1 2*log\\/ x /| 2|log\\/ x /| 2/ ___\ atan |----------|*|- - + ------------|*|-- - ------------ + -------------- - ------------| 3*|- - + ------------|*|-- - ------------ + ---------|*atan|----------| | 1 2*log\\/ x /| |log\\/ x /| / ___\ atan |----------|*|- - + ------------|*|-- - ------------ + ---------|*log\\/ x /|
| \ 2 + x / | 3 3 2 2| |- - + ------------| |- - + ------------| *atan |----------|*log \\/ x / \ 2 + x / \ x 2 + x / | 2 2 2 x*(2 + x) | \ x 2 + x / | 2 2 x*(2 + x)| \ 2 + x / 3*|- - + ------------| *atan|----------|*log\\/ x / \ 2 + x / \ x 2 + x / | 2 2 x*(2 + x)| |
| \x (2 + x) x *(2 + x) x*(2 + x) / \ x 2 + x / \ x 2 + x / \ 2 + x / \x x (2 + x) / \x (2 + x) / \ x 2 + x / \ 2 + x / \x (2 + x) / |
3*|---------------------------------------------------------------- - ----------------------------- - --------------------------------------------------- + ------------------------------------------------------------------------------------------ + ----------------------------------------------------------------------- + --------------------------------------------------- - ---------------------------------------------------------------------------------|
| 2 2 2 / 2/ ___\\ / 2/ ___\\ 2 / 2/ ___\\ |
| / 2/ ___\\ / 2/ ___\\ | log \\/ x /| 2 | log \\/ x /| / 2/ ___\\ | log \\/ x /| 2 |
| | log \\/ x /| 2 | log \\/ x /| 4 4*|1 + -----------|*(2 + x) 2*|1 + -----------|*(2 + x) | log \\/ x /| 3 |1 + -----------|*(2 + x) |
| 4*|1 + -----------| *(2 + x) |1 + -----------| *(2 + x) | 2 | | 2 | 2*|1 + -----------| *(2 + x) | 2 | |
| | 2 | | 2 | \ (2 + x) / \ (2 + x) / | 2 | \ (2 + x) / |
\ \ (2 + x) / \ (2 + x) / \ (2 + x) / /
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
/ 2/ ___\\
| log \\/ x /|
|1 + -----------|*(2 + x)
| 2 |
\ (2 + x) /
$$\frac{3 \left(\frac{\left(- \frac{12 \log{\left(\sqrt{x} \right)}}{\left(x + 2\right)^{3}} + \frac{6}{x \left(x + 2\right)^{2}} + \frac{3}{x^{2} \left(x + 2\right)} + \frac{2}{x^{3}}\right) \operatorname{atan}^{2}{\left(\frac{\log{\left(\sqrt{x} \right)}}{x + 2} \right)}}{2} + \frac{3 \left(\frac{2 \log{\left(\sqrt{x} \right)}}{x + 2} - \frac{1}{x}\right) \left(- \frac{4 \log{\left(\sqrt{x} \right)}}{\left(x + 2\right)^{2}} + \frac{2}{x \left(x + 2\right)} + \frac{1}{x^{2}}\right) \operatorname{atan}{\left(\frac{\log{\left(\sqrt{x} \right)}}{x + 2} \right)}}{2 \left(1 + \frac{\log{\left(\sqrt{x} \right)}^{2}}{\left(x + 2\right)^{2}}\right) \left(x + 2\right)} - \frac{\left(\frac{2 \log{\left(\sqrt{x} \right)}}{x + 2} - \frac{1}{x}\right) \left(- \frac{4 \log{\left(\sqrt{x} \right)}}{\left(x + 2\right)^{2}} + \frac{2}{x \left(x + 2\right)} + \frac{1}{x^{2}}\right) \log{\left(\sqrt{x} \right)} \operatorname{atan}^{2}{\left(\frac{\log{\left(\sqrt{x} \right)}}{x + 2} \right)}}{\left(1 + \frac{\log{\left(\sqrt{x} \right)}^{2}}{\left(x + 2\right)^{2}}\right) \left(x + 2\right)^{2}} + \frac{\left(\frac{2 \log{\left(\sqrt{x} \right)}}{x + 2} - \frac{1}{x}\right) \left(\frac{12 \log{\left(\sqrt{x} \right)}^{2}}{\left(x + 2\right)^{2}} - \frac{8 \log{\left(\sqrt{x} \right)}}{x \left(x + 2\right)} - \frac{2 \log{\left(\sqrt{x} \right)}}{x^{2}} + \frac{1}{x^{2}}\right) \operatorname{atan}^{2}{\left(\frac{\log{\left(\sqrt{x} \right)}}{x + 2} \right)}}{4 \left(1 + \frac{\log{\left(\sqrt{x} \right)}^{2}}{\left(x + 2\right)^{2}}\right) \left(x + 2\right)^{2}} - \frac{\left(\frac{2 \log{\left(\sqrt{x} \right)}}{x + 2} - \frac{1}{x}\right)^{3}}{4 \left(1 + \frac{\log{\left(\sqrt{x} \right)}^{2}}{\left(x + 2\right)^{2}}\right)^{2} \left(x + 2\right)^{2}} + \frac{3 \left(\frac{2 \log{\left(\sqrt{x} \right)}}{x + 2} - \frac{1}{x}\right)^{3} \log{\left(\sqrt{x} \right)} \operatorname{atan}{\left(\frac{\log{\left(\sqrt{x} \right)}}{x + 2} \right)}}{2 \left(1 + \frac{\log{\left(\sqrt{x} \right)}^{2}}{\left(x + 2\right)^{2}}\right)^{2} \left(x + 2\right)^{3}} - \frac{\left(\frac{2 \log{\left(\sqrt{x} \right)}}{x + 2} - \frac{1}{x}\right)^{3} \log{\left(\sqrt{x} \right)}^{2} \operatorname{atan}^{2}{\left(\frac{\log{\left(\sqrt{x} \right)}}{x + 2} \right)}}{\left(1 + \frac{\log{\left(\sqrt{x} \right)}^{2}}{\left(x + 2\right)^{2}}\right)^{2} \left(x + 2\right)^{4}}\right)}{\left(1 + \frac{\log{\left(\sqrt{x} \right)}^{2}}{\left(x + 2\right)^{2}}\right) \left(x + 2\right)}$$
Gráfico