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
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Expresiones idénticas
- y=arctg^ tres (ln(chx)+(uno / dos ch^2*x))
- y es igual a arctg al cubo (ln(chx) más (1 dividir por 2ch al cuadrado multiplicar por x))
- y es igual a arctg en el grado tres (ln(chx) más (uno dividir por dos ch al cuadrado multiplicar por x))
- y=arctg3(ln(chx)+(1/2ch2*x))
- y=arctg3lnchx+1/2ch2*x
- y=arctg³(ln(chx)+(1/2ch²*x))
- y=arctg en el grado 3(ln(chx)+(1/2ch en el grado 2*x))
- y=arctg^3(ln(chx)+(1/2ch^2x))
- y=arctg3(ln(chx)+(1/2ch2x))
- y=arctg3lnchx+1/2ch2x
- y=arctg^3lnchx+1/2ch^2x
- y=arctg^3(ln(chx)+(1 dividir por 2ch^2*x))
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Expresiones semejantes
- y=arctg^3(ln(chx)-(1/2ch^2*x))
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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=arctg^3(ln(chx)+(1/2ch^2*x))
Solución
Ha introducido
[src]
/ 2 \
3| cosh (x)|
atan |log(cosh(x)) + --------|
\ 2 /
$$\operatorname{atan}^{3}{\left(\log{\left(\cosh{\left(x \right)} \right)} + \frac{\cosh^{2}{\left(x \right)}}{2} \right)}$$
atan(log(cosh(x)) + cosh(x)^2/2)^3
Primera derivada
[src]
/ 2 \
2| cosh (x)| /sinh(x) \
3*atan |log(cosh(x)) + --------|*|------- + cosh(x)*sinh(x)|
\ 2 / \cosh(x) /
------------------------------------------------------------
2
/ 2 \
| cosh (x)|
1 + |log(cosh(x)) + --------|
\ 2 /
$$\frac{3 \left(\sinh{\left(x \right)} \cosh{\left(x \right)} + \frac{\sinh{\left(x \right)}}{\cosh{\left(x \right)}}\right) \operatorname{atan}^{2}{\left(\log{\left(\cosh{\left(x \right)} \right)} + \frac{\cosh^{2}{\left(x \right)}}{2} \right)}}{\left(\log{\left(\cosh{\left(x \right)} \right)} + \frac{\cosh^{2}{\left(x \right)}}{2}\right)^{2} + 1}$$
Segunda derivada
[src]
/ 2 2 / 2 \\
| / 1 \ 2 / 1 \ 2 / 2 \ |cosh (x) ||
|/ 2 \ / 2 \ 8*|------- + cosh(x)| *sinh (x) 4*|------- + cosh(x)| *sinh (x)*\cosh (x) + 2*log(cosh(x))/*atan|-------- + log(cosh(x))|| / 2 \
|| 2 2 sinh (x)| |cosh (x) | \cosh(x) / \cosh(x) / \ 2 /| |cosh (x) |
12*||1 + cosh (x) + sinh (x) - --------|*atan|-------- + log(cosh(x))| + -------------------------------- - -----------------------------------------------------------------------------------------|*atan|-------- + log(cosh(x))|
|| 2 | \ 2 / 2 2 | \ 2 /
|\ cosh (x)/ / 2 \ / 2 \ |
\ 4 + \cosh (x) + 2*log(cosh(x))/ 4 + \cosh (x) + 2*log(cosh(x))/ /
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
2
/ 2 \
4 + \cosh (x) + 2*log(cosh(x))/
$$\frac{12 \left(\left(\sinh^{2}{\left(x \right)} - \frac{\sinh^{2}{\left(x \right)}}{\cosh^{2}{\left(x \right)}} + \cosh^{2}{\left(x \right)} + 1\right) \operatorname{atan}{\left(\log{\left(\cosh{\left(x \right)} \right)} + \frac{\cosh^{2}{\left(x \right)}}{2} \right)} - \frac{4 \left(2 \log{\left(\cosh{\left(x \right)} \right)} + \cosh^{2}{\left(x \right)}\right) \left(\cosh{\left(x \right)} + \frac{1}{\cosh{\left(x \right)}}\right)^{2} \sinh^{2}{\left(x \right)} \operatorname{atan}{\left(\log{\left(\cosh{\left(x \right)} \right)} + \frac{\cosh^{2}{\left(x \right)}}{2} \right)}}{\left(2 \log{\left(\cosh{\left(x \right)} \right)} + \cosh^{2}{\left(x \right)}\right)^{2} + 4} + \frac{8 \left(\cosh{\left(x \right)} + \frac{1}{\cosh{\left(x \right)}}\right)^{2} \sinh^{2}{\left(x \right)}}{\left(2 \log{\left(\cosh{\left(x \right)} \right)} + \cosh^{2}{\left(x \right)}\right)^{2} + 4}\right) \operatorname{atan}{\left(\log{\left(\cosh{\left(x \right)} \right)} + \frac{\cosh^{2}{\left(x \right)}}{2} \right)}}{\left(2 \log{\left(\cosh{\left(x \right)} \right)} + \cosh^{2}{\left(x \right)}\right)^{2} + 4}$$
Tercera derivada
[src]
/ / 2 \ / 2 \ / 2 \ / 2 \ \
| 3 3 / 2 \ / 1 \ | 2 2 sinh (x)| |cosh (x) | 3 / 2 \ 2|cosh (x) | / 1 \ / 2 \ | 2 2 sinh (x)| 3 2 / 2 \ |
| / 1 \ 2 / 1 \ 2|cosh (x) | 2 12*|------- + cosh(x)|*|1 + cosh (x) + sinh (x) - --------|*atan|-------- + log(cosh(x))| / 1 \ 2 / 2 \ |cosh (x) | 6*atan |-------- + log(cosh(x))|*|------- + cosh(x)|*\cosh (x) + 2*log(cosh(x))/*|1 + cosh (x) + sinh (x) - --------| / 1 \ / 2 \ 2|cosh (x) | 2 |
| / 2 \ / 2 \ 16*|------- + cosh(x)| *sinh (x) 4*|------- + cosh(x)| *atan |-------- + log(cosh(x))|*sinh (x) \cosh(x) / | 2 | \ 2 / 48*|------- + cosh(x)| *sinh (x)*\cosh (x) + 2*log(cosh(x))/*atan|-------- + log(cosh(x))| \ 2 / \cosh(x) / | 2 | 16*|------- + cosh(x)| *\cosh (x) + 2*log(cosh(x))/ *atan |-------- + log(cosh(x))|*sinh (x)|
| 2|cosh (x) | | 1 sinh (x)| \cosh(x) / \cosh(x) / \ 2 / \ cosh (x)/ \cosh(x) / \ 2 / \ cosh (x)/ \cosh(x) / \ 2 / |
24*|atan |-------- + log(cosh(x))|*|- ------- + 2*cosh(x) + --------| + ----------------------------------- - -------------------------------------------------------------- + ----------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------ - --------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------|*sinh(x)
| \ 2 / | cosh(x) 3 | 2 2 2 2 2 2 |
| \ cosh (x)/ / 2\ / 2 \ / 2 \ / 2\ / 2 \ / 2\ |
| | / 2 \ | 4 + \cosh (x) + 2*log(cosh(x))/ 4 + \cosh (x) + 2*log(cosh(x))/ | / 2 \ | 4 + \cosh (x) + 2*log(cosh(x))/ | / 2 \ | |
\ \4 + \cosh (x) + 2*log(cosh(x))/ / \4 + \cosh (x) + 2*log(cosh(x))/ / \4 + \cosh (x) + 2*log(cosh(x))/ / /
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
2
/ 2 \
4 + \cosh (x) + 2*log(cosh(x))/
$$\frac{24 \left(\left(\frac{\sinh^{2}{\left(x \right)}}{\cosh^{3}{\left(x \right)}} + 2 \cosh{\left(x \right)} - \frac{1}{\cosh{\left(x \right)}}\right) \operatorname{atan}^{2}{\left(\log{\left(\cosh{\left(x \right)} \right)} + \frac{\cosh^{2}{\left(x \right)}}{2} \right)} - \frac{6 \left(2 \log{\left(\cosh{\left(x \right)} \right)} + \cosh^{2}{\left(x \right)}\right) \left(\cosh{\left(x \right)} + \frac{1}{\cosh{\left(x \right)}}\right) \left(\sinh^{2}{\left(x \right)} - \frac{\sinh^{2}{\left(x \right)}}{\cosh^{2}{\left(x \right)}} + \cosh^{2}{\left(x \right)} + 1\right) \operatorname{atan}^{2}{\left(\log{\left(\cosh{\left(x \right)} \right)} + \frac{\cosh^{2}{\left(x \right)}}{2} \right)}}{\left(2 \log{\left(\cosh{\left(x \right)} \right)} + \cosh^{2}{\left(x \right)}\right)^{2} + 4} - \frac{4 \left(\cosh{\left(x \right)} + \frac{1}{\cosh{\left(x \right)}}\right)^{3} \sinh^{2}{\left(x \right)} \operatorname{atan}^{2}{\left(\log{\left(\cosh{\left(x \right)} \right)} + \frac{\cosh^{2}{\left(x \right)}}{2} \right)}}{\left(2 \log{\left(\cosh{\left(x \right)} \right)} + \cosh^{2}{\left(x \right)}\right)^{2} + 4} + \frac{12 \left(\cosh{\left(x \right)} + \frac{1}{\cosh{\left(x \right)}}\right) \left(\sinh^{2}{\left(x \right)} - \frac{\sinh^{2}{\left(x \right)}}{\cosh^{2}{\left(x \right)}} + \cosh^{2}{\left(x \right)} + 1\right) \operatorname{atan}{\left(\log{\left(\cosh{\left(x \right)} \right)} + \frac{\cosh^{2}{\left(x \right)}}{2} \right)}}{\left(2 \log{\left(\cosh{\left(x \right)} \right)} + \cosh^{2}{\left(x \right)}\right)^{2} + 4} + \frac{16 \left(2 \log{\left(\cosh{\left(x \right)} \right)} + \cosh^{2}{\left(x \right)}\right)^{2} \left(\cosh{\left(x \right)} + \frac{1}{\cosh{\left(x \right)}}\right)^{3} \sinh^{2}{\left(x \right)} \operatorname{atan}^{2}{\left(\log{\left(\cosh{\left(x \right)} \right)} + \frac{\cosh^{2}{\left(x \right)}}{2} \right)}}{\left(\left(2 \log{\left(\cosh{\left(x \right)} \right)} + \cosh^{2}{\left(x \right)}\right)^{2} + 4\right)^{2}} - \frac{48 \left(2 \log{\left(\cosh{\left(x \right)} \right)} + \cosh^{2}{\left(x \right)}\right) \left(\cosh{\left(x \right)} + \frac{1}{\cosh{\left(x \right)}}\right)^{3} \sinh^{2}{\left(x \right)} \operatorname{atan}{\left(\log{\left(\cosh{\left(x \right)} \right)} + \frac{\cosh^{2}{\left(x \right)}}{2} \right)}}{\left(\left(2 \log{\left(\cosh{\left(x \right)} \right)} + \cosh^{2}{\left(x \right)}\right)^{2} + 4\right)^{2}} + \frac{16 \left(\cosh{\left(x \right)} + \frac{1}{\cosh{\left(x \right)}}\right)^{3} \sinh^{2}{\left(x \right)}}{\left(\left(2 \log{\left(\cosh{\left(x \right)} \right)} + \cosh^{2}{\left(x \right)}\right)^{2} + 4\right)^{2}}\right) \sinh{\left(x \right)}}{\left(2 \log{\left(\cosh{\left(x \right)} \right)} + \cosh^{2}{\left(x \right)}\right)^{2} + 4}$$
Gráfico