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=arctg((tres x-x^3)/(uno -3x^ dos))
- y es igual a arctg((3x menos x al cubo ) dividir por (1 menos 3x al cuadrado ))
- y es igual a arctg((tres x menos x al cubo ) dividir por (uno menos 3x en el grado dos))
- y=arctg((3x-x3)/(1-3x2))
- y=arctg3x-x3/1-3x2
- y=arctg((3x-x³)/(1-3x²))
- y=arctg((3x-x en el grado 3)/(1-3x en el grado 2))
- y=arctg3x-x^3/1-3x^2
- y=arctg((3x-x^3) dividir por (1-3x^2))
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Expresiones semejantes
- y=arctg((3x-x^3)/(1+3x^2))
- y=arctg((3x+x^3)/(1-3x^2))
Derivada de y=arctg((3x-x^3)/(1-3x^2))
Solución
Ha introducido
[src]
/ 3\
|3*x - x |
atan|--------|
| 2|
\1 - 3*x /
$$\operatorname{atan}{\left(\frac{- x^{3} + 3 x}{1 - 3 x^{2}} \right)}$$
atan((3*x - x^3)/(1 - 3*x^2))
Primera derivada
[src]
2 / 3\
3 - 3*x 6*x*\3*x - x /
-------- + --------------
2 2
1 - 3*x / 2\
\1 - 3*x /
-------------------------
2
/ 3\
\3*x - x /
1 + -----------
2
/ 2\
\1 - 3*x /
$$\frac{\frac{6 x \left(- x^{3} + 3 x\right)}{\left(1 - 3 x^{2}\right)^{2}} + \frac{3 - 3 x^{2}}{1 - 3 x^{2}}}{1 + \frac{\left(- x^{3} + 3 x\right)^{2}}{\left(1 - 3 x^{2}\right)^{2}}}$$
Segunda derivada
[src]
/ 2 \
| / 2 / 2\\ |
| | 2 2*x *\-3 + x /| / 2\|
| 3*|1 - x + --------------| *\-3 + x /|
| 2 / 2\ 2 / 2\ | 2 | |
| -3 + x 6*\-1 + x / 12*x *\-3 + x / \ -1 + 3*x / |
6*x*|1 - --------- - ----------- + --------------- - --------------------------------------|
| 2 2 2 / 2\ |
| -1 + 3*x -1 + 3*x / 2\ | 2 / 2\ | 2 |
| \-1 + 3*x / | x *\-3 + x / | / 2\ |
| |1 + -------------|*\-1 + 3*x / |
| | 2| |
| | / 2\ | |
\ \ \-1 + 3*x / / /
--------------------------------------------------------------------------------------------
/ 2\
| 2 / 2\ |
| x *\-3 + x / | / 2\
|1 + -------------|*\-1 + 3*x /
| 2|
| / 2\ |
\ \-1 + 3*x / /
$$\frac{6 x \left(\frac{12 x^{2} \left(x^{2} - 3\right)}{\left(3 x^{2} - 1\right)^{2}} - \frac{x^{2} - 3}{3 x^{2} - 1} - \frac{3 \left(x^{2} - 3\right) \left(\frac{2 x^{2} \left(x^{2} - 3\right)}{3 x^{2} - 1} - x^{2} + 1\right)^{2}}{\left(3 x^{2} - 1\right)^{2} \left(\frac{x^{2} \left(x^{2} - 3\right)^{2}}{\left(3 x^{2} - 1\right)^{2}} + 1\right)} - \frac{6 \left(x^{2} - 1\right)}{3 x^{2} - 1} + 1\right)}{\left(3 x^{2} - 1\right) \left(\frac{x^{2} \left(x^{2} - 3\right)^{2}}{\left(3 x^{2} - 1\right)^{2}} + 1\right)}$$
Tercera derivada
[src]
/ / 2 2 \ \
| / 2 / 2\\ | 2 2 / 2\ 4 / 2\ 2 / 2\ / 2\| 3 / 2 / 2\\ / 2 / 2\ 2 / 2\\|
| | 2 2*x *\-3 + x /| | / 2\ 2 / 2\ 2*x *\-3 + x / 36*x *\-3 + x / 24*x *\-1 + x /*\-3 + x /| 2 / 2 / 2\\ 2 / 2\ | 2 2*x *\-3 + x /| | -3 + x 6*\-1 + x / 12*x *\-3 + x /||
| 3*|1 - x + --------------|*|3*\-1 + x / + 2*x *\-3 + x / - --------------- + ---------------- - -------------------------| 2 / 2\ | 2 2*x *\-3 + x /| 12*x *\-3 + x /*|1 - x + --------------|*|1 - --------- - ----------- + ---------------||
| | 2 | | 2 2 2 | 36*x *\-3 + x / *|1 - x + --------------| | 2 | | 2 2 2 ||
| 2 / 2\ 4 / 2\ 2 / 2\ 2 / 2\ \ -1 + 3*x / | -1 + 3*x / 2\ -1 + 3*x | | 2 | \ -1 + 3*x / | -1 + 3*x -1 + 3*x / 2\ ||
| 18*x 9*\-1 + x / 216*x *\-3 + x / 36*x *\-3 + x / 108*x *\-1 + x / \ \-1 + 3*x / / \ -1 + 3*x / \ \-1 + 3*x / /|
6*|1 - --------- - ----------- - ---------------- + --------------- + ---------------- + ---------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------- + -----------------------------------------------------------------------------------------|
| 2 2 3 2 2 / 2\ 2 / 2\ |
| -1 + 3*x -1 + 3*x / 2\ / 2\ / 2\ | 2 / 2\ | 2 / 2\ | 2 / 2\ | 2 |
| \-1 + 3*x / \-1 + 3*x / \-1 + 3*x / | x *\-3 + x / | / 2\ | 2 / 2\ | 4 | x *\-3 + x / | / 2\ |
| |1 + -------------|*\-1 + 3*x / | x *\-3 + x / | / 2\ |1 + -------------|*\-1 + 3*x / |
| | 2| |1 + -------------| *\-1 + 3*x / | 2| |
| | / 2\ | | 2| | / 2\ | |
| \ \-1 + 3*x / / | / 2\ | \ \-1 + 3*x / / |
\ \ \-1 + 3*x / / /
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
/ 2\
| 2 / 2\ |
| x *\-3 + x / | / 2\
|1 + -------------|*\-1 + 3*x /
| 2|
| / 2\ |
\ \-1 + 3*x / /
$$\frac{6 \left(- \frac{216 x^{4} \left(x^{2} - 3\right)}{\left(3 x^{2} - 1\right)^{3}} - \frac{36 x^{2} \left(x^{2} - 3\right)^{2} \left(\frac{2 x^{2} \left(x^{2} - 3\right)}{3 x^{2} - 1} - x^{2} + 1\right)^{3}}{\left(3 x^{2} - 1\right)^{4} \left(\frac{x^{2} \left(x^{2} - 3\right)^{2}}{\left(3 x^{2} - 1\right)^{2}} + 1\right)^{2}} + \frac{36 x^{2} \left(x^{2} - 3\right)}{\left(3 x^{2} - 1\right)^{2}} + \frac{12 x^{2} \left(x^{2} - 3\right) \left(\frac{2 x^{2} \left(x^{2} - 3\right)}{3 x^{2} - 1} - x^{2} + 1\right) \left(\frac{12 x^{2} \left(x^{2} - 3\right)}{\left(3 x^{2} - 1\right)^{2}} - \frac{x^{2} - 3}{3 x^{2} - 1} - \frac{6 \left(x^{2} - 1\right)}{3 x^{2} - 1} + 1\right)}{\left(3 x^{2} - 1\right)^{2} \left(\frac{x^{2} \left(x^{2} - 3\right)^{2}}{\left(3 x^{2} - 1\right)^{2}} + 1\right)} + \frac{108 x^{2} \left(x^{2} - 1\right)}{\left(3 x^{2} - 1\right)^{2}} - \frac{18 x^{2}}{3 x^{2} - 1} - \frac{9 \left(x^{2} - 1\right)}{3 x^{2} - 1} + 1 + \frac{3 \left(\frac{2 x^{2} \left(x^{2} - 3\right)}{3 x^{2} - 1} - x^{2} + 1\right) \left(\frac{36 x^{4} \left(x^{2} - 3\right)^{2}}{\left(3 x^{2} - 1\right)^{2}} - \frac{2 x^{2} \left(x^{2} - 3\right)^{2}}{3 x^{2} - 1} - \frac{24 x^{2} \left(x^{2} - 3\right) \left(x^{2} - 1\right)}{3 x^{2} - 1} + 2 x^{2} \left(x^{2} - 3\right) + 3 \left(x^{2} - 1\right)^{2}\right)}{\left(3 x^{2} - 1\right)^{2} \left(\frac{x^{2} \left(x^{2} - 3\right)^{2}}{\left(3 x^{2} - 1\right)^{2}} + 1\right)}\right)}{\left(3 x^{2} - 1\right) \left(\frac{x^{2} \left(x^{2} - 3\right)^{2}}{\left(3 x^{2} - 1\right)^{2}} + 1\right)}$$
Gráfico