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 1/(x+1)^2
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Derivada de (x+3)/(x-2)
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Derivada de (x+4)^2*(x+1)+9
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Derivada de e^(2-x)
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Expresiones idénticas
- е^(arctg(x- uno)/(x+ uno))
- е en el grado (arctg(x menos 1) dividir por (x más 1))
- е en el grado (arctg(x menos uno) dividir por (x más uno))
- е(arctg(x-1)/(x+1))
- еarctgx-1/x+1
- е^arctgx-1/x+1
- е^(arctg(x-1) dividir por (x+1))
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Expresiones semejantes
- е^(arctg(x+1)/(x+1))
- е^(arctg(x-1)/(x-1))
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Expresiones con funciones
- arctg
- arctg^3*4x*3^sinx
- arctg(sqrt(x))
- arctg(cos(x))
- arctg(x+cosx)
- arctg^2(1/x)
Derivada de е^(arctg(x-1)/(x+1))
Solución
Ha introducido
[src]
atan(x - 1)
-----------
x + 1
E
$$e^{\frac{\operatorname{atan}{\left(x - 1 \right)}}{x + 1}}$$
E^(atan(x - 1)/(x + 1))
Primera derivada
[src]
atan(x - 1)
-----------
/ 1 atan(x - 1)\ x + 1
|---------------------- - -----------|*e
|/ 2\ 2 |
\\1 + (x - 1) /*(x + 1) (x + 1) /
$$\left(\frac{1}{\left(x + 1\right) \left(\left(x - 1\right)^{2} + 1\right)} - \frac{\operatorname{atan}{\left(x - 1 \right)}}{\left(x + 1\right)^{2}}\right) e^{\frac{\operatorname{atan}{\left(x - 1 \right)}}{x + 1}}$$
Segunda derivada
[src]
/ 2 \
|/ 1 atan(-1 + x)\ |
||------------- - ------------| | atan(-1 + x)
|| 2 1 + x | | ------------
|\1 + (-1 + x) / 2 2*(-1 + x) 2*atan(-1 + x)| 1 + x
|------------------------------- - ----------------------- - ---------------- + --------------|*e
| 1 + x / 2\ 2 2 |
| (1 + x)*\1 + (-1 + x) / / 2\ (1 + x) |
\ \1 + (-1 + x) / /
-------------------------------------------------------------------------------------------------------------
1 + x
$$\frac{\left(- \frac{2 \left(x - 1\right)}{\left(\left(x - 1\right)^{2} + 1\right)^{2}} + \frac{\left(\frac{1}{\left(x - 1\right)^{2} + 1} - \frac{\operatorname{atan}{\left(x - 1 \right)}}{x + 1}\right)^{2}}{x + 1} - \frac{2}{\left(x + 1\right) \left(\left(x - 1\right)^{2} + 1\right)} + \frac{2 \operatorname{atan}{\left(x - 1 \right)}}{\left(x + 1\right)^{2}}\right) e^{\frac{\operatorname{atan}{\left(x - 1 \right)}}{x + 1}}}{x + 1}$$
Tercera derivada
[src]
/ 3 / 1 atan(-1 + x)\ / 1 -1 + x atan(-1 + x)\ \
| / 1 atan(-1 + x)\ 6*|------------- - ------------|*|----------------------- + ---------------- - ------------| |
| |------------- - ------------| | 2 1 + x | | / 2\ 2 2 | | atan(-1 + x)
| | 2 1 + x | 2 \1 + (-1 + x) / |(1 + x)*\1 + (-1 + x) / / 2\ (1 + x) | | ------------
| 2 \1 + (-1 + x) / 6*atan(-1 + x) 6 8*(-1 + x) \ \1 + (-1 + x) / / 6*(-1 + x) | 1 + x
|- ---------------- + ------------------------------- - -------------- + ------------------------ + ---------------- - -------------------------------------------------------------------------------------------- + ------------------------|*e
| 2 2 3 2 / 2\ 3 1 + x 2|
| / 2\ (1 + x) (1 + x) (1 + x) *\1 + (-1 + x) / / 2\ / 2\ |
\ \1 + (-1 + x) / \1 + (-1 + x) / (1 + x)*\1 + (-1 + x) / /
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
1 + x
$$\frac{\left(\frac{8 \left(x - 1\right)^{2}}{\left(\left(x - 1\right)^{2} + 1\right)^{3}} + \frac{6 \left(x - 1\right)}{\left(x + 1\right) \left(\left(x - 1\right)^{2} + 1\right)^{2}} - \frac{2}{\left(\left(x - 1\right)^{2} + 1\right)^{2}} - \frac{6 \left(\frac{1}{\left(x - 1\right)^{2} + 1} - \frac{\operatorname{atan}{\left(x - 1 \right)}}{x + 1}\right) \left(\frac{x - 1}{\left(\left(x - 1\right)^{2} + 1\right)^{2}} + \frac{1}{\left(x + 1\right) \left(\left(x - 1\right)^{2} + 1\right)} - \frac{\operatorname{atan}{\left(x - 1 \right)}}{\left(x + 1\right)^{2}}\right)}{x + 1} + \frac{\left(\frac{1}{\left(x - 1\right)^{2} + 1} - \frac{\operatorname{atan}{\left(x - 1 \right)}}{x + 1}\right)^{3}}{\left(x + 1\right)^{2}} + \frac{6}{\left(x + 1\right)^{2} \left(\left(x - 1\right)^{2} + 1\right)} - \frac{6 \operatorname{atan}{\left(x - 1 \right)}}{\left(x + 1\right)^{3}}\right) e^{\frac{\operatorname{atan}{\left(x - 1 \right)}}{x + 1}}}{x + 1}$$
Gráfico