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
-
¿Cómo usar?
- Derivada de:
-
Derivada de -2*y
-
Derivada de 3^2*x
-
Derivada de 2*x+8/x
-
Derivada de -1/y
- Integral de d{x}:
- x/((x+1)(x^2+1))
-
Expresiones idénticas
- x/((x+ uno)(x^ dos + uno))
- x dividir por ((x más 1)(x al cuadrado más 1))
- x dividir por ((x más uno)(x en el grado dos más uno))
- x/((x+1)(x2+1))
- x/x+1x2+1
- x/((x+1)(x²+1))
- x/((x+1)(x en el grado 2+1))
- x/x+1x^2+1
- x dividir por ((x+1)(x^2+1))
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Expresiones semejantes
- x/((x+1)(x^2-1))
- x/((x-1)(x^2+1))
Derivada de x/((x+1)(x^2+1))
Solución
Ha introducido
[src]
x
----------------
/ 2 \
(x + 1)*\x + 1/
$$\frac{x}{\left(x + 1\right) \left(x^{2} + 1\right)}$$
x/(((x + 1)*(x^2 + 1)))
Solución detallada
-
Se aplica la regla de la derivada parcial:
y .
Para calcular :
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Según el principio, aplicamos: tenemos
Para calcular :
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Se aplica la regla de la derivada de una multiplicación:
; calculamos :
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diferenciamos miembro por miembro:
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La derivada de una constante es igual a cero.
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Según el principio, aplicamos: tenemos
Como resultado de:
-
; calculamos :
-
diferenciamos miembro por miembro:
-
La derivada de una constante es igual a cero.
-
Según el principio, aplicamos: tenemos
Como resultado de:
-
Como resultado de:
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Ahora aplicamos la regla de la derivada de una divesión:
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Respuesta:
Primera derivada
[src]
/ 2 \
1 x*\-1 - x - 2*x*(x + 1)/
---------------- + -------------------------
/ 2 \ 2
(x + 1)*\x + 1/ 2 / 2 \
(x + 1) *\x + 1/
$$\frac{x \left(- x^{2} - 2 x \left(x + 1\right) - 1\right)}{\left(x + 1\right)^{2} \left(x^{2} + 1\right)^{2}} + \frac{1}{\left(x + 1\right) \left(x^{2} + 1\right)}$$
Segunda derivada
[src]
/ 2 / 2 \\
2 | 1 + x + 2*x*(1 + x) / 1 2*x \ / 2 \ 2*x*\1 + x + 2*x*(1 + x)/|
-2 - 2*x + x*|-2 - 6*x + -------------------- + |----- + ------|*\1 + x + 2*x*(1 + x)/ + --------------------------| - 4*x*(1 + x)
| 1 + x |1 + x 2| 2 |
\ \ 1 + x / 1 + x /
------------------------------------------------------------------------------------------------------------------------------------
2
2 / 2\
(1 + x) *\1 + x /
$$\frac{- 2 x^{2} - 4 x \left(x + 1\right) + x \left(- 6 x + \frac{2 x \left(x^{2} + 2 x \left(x + 1\right) + 1\right)}{x^{2} + 1} + \left(\frac{2 x}{x^{2} + 1} + \frac{1}{x + 1}\right) \left(x^{2} + 2 x \left(x + 1\right) + 1\right) - 2 + \frac{x^{2} + 2 x \left(x + 1\right) + 1}{x + 1}\right) - 2}{\left(x + 1\right)^{2} \left(x^{2} + 1\right)^{2}}$$
4-я производная
[src]
/ / / 2 \ / 2 \ \ \
| | / 2 \ | 1 1 4*x 2*x | / 2 \ | 1 1 4*x 2*x | | |
| | / 1 2*x \ / 2 \ / 1 2*x \ / 2 \ / 1 2*x \ 2*\1 + x + 2*x*(1 + x)/*|-------- - ------ + --------- + ----------------| / 1 2*x \ 4*x*\1 + x + 2*x*(1 + x)/*|-------- - ------ + --------- + ----------------| 2 / 1 2*x \ / 2 \ / 1 2*x \ / 2 \| / 1 2*x \ / 2 \ / 1 2*x \ / 2 \|
| | |----- + ------|*\1 + x + 2*x*(1 + x)/ |----- + ------|*\1 + x + 2*x*(1 + x)/ 2*(1 + 3*x)*|----- + ------| | 2 2 2 / 2\| 4*x*(1 + 3*x)*|----- + ------| | 2 2 2 / 2\| 4*x *|----- + ------|*\1 + x + 2*x*(1 + x)/ 2*x*|----- + ------|*\1 + x + 2*x*(1 + x)/| 2*|----- + ------|*\1 + x + 2*x*(1 + x)/ 4*x*|----- + ------|*\1 + x + 2*x*(1 + x)/|
| | / 2 \ / 3 2 \ / 2 \ |1 + x 2| |1 + x 2| 2 / 2 \ / 2 \ |1 + x 2| |(1 + x) 1 + x / 2\ (1 + x)*\1 + x /| 3 / 2 \ |1 + x 2| |(1 + x) 1 + x / 2\ (1 + x)*\1 + x /| |1 + x 2| / 2 \ 2 / 2 \ |1 + x 2| | / 2 \ / 2 \ / 2 \ 2 / 2 \ |1 + x 2| / 2 \ |1 + x 2| |
| | 18 12*(1 + 3*x) | 1 1 4*x 2*x | / 2 \ | 1 1 4*x 8*x 2*x 4*x | 6*\1 + x + 2*x*(1 + x)/ 8*(1 + 3*x) 36*x \ 1 + x / \ 1 + x / 48*x *(1 + 3*x) 18*x*\1 + x + 2*x*(1 + x)/ 6*\1 + x + 2*x*(1 + x)/ \ 1 + x / \ \1 + x / / 48*x *\1 + x + 2*x*(1 + x)/ 32*x*(1 + 3*x) \ 1 + x / \ \1 + x / / \ 1 + x / 18*x*\1 + x + 2*x*(1 + x)/ 36*x *\1 + x + 2*x*(1 + x)/ \ 1 + x / | 6*\1 + x + 2*x*(1 + x)/ / 2 \ | 1 1 4*x 2*x | 4*\1 + x + 2*x*(1 + x)/ / 1 2*x \ 12*(1 + 3*x) 24*x *\1 + x + 2*x*(1 + x)/ \ 1 + x / 24*x*(1 + 3*x) 16*x*\1 + x + 2*x*(1 + x)/ \ 1 + x / |
2*|-12 + x*|----- - ------------ - 4*(1 + 3*x)*|-------- - ------ + --------- + ----------------| + 3*\1 + x + 2*x*(1 + x)/*|-------- - ---------------- - --------- + --------- + ----------------- + -----------------| + ------------------------ + ----------- + ------ + --------------------------------------- - --------------------------------------- - --------------- - --------------------------- - ------------------------ - ---------------------------- + --------------------------------------------------------------------------- + ---------------------------- - ---------------- - ------------------------------ + ----------------------------------------------------------------------------- + -------------------------------------------- + --------------------------- + ---------------------------- + -------------------------------------------| - ------------------------ - 4*\1 + x + 2*x*(1 + x)/*|-------- - ------ + --------- + ----------------| + ------------------------ + 4*(1 + 3*x)*|----- + ------| + ------------ - ---------------------------- - ----------------------------------------- + -------------- - --------------------------- - -------------------------------------------|
| |1 + x 2 | 2 2 2 / 2\| | 3 / 2\ 2 3 2 / 2\ 2| 3 2 2 2 2 2 2 / 2\ 1 + x 1 + x 3 / 2\ 2 2 2 2 / 2\ 2 / 2\ | 2 | 2 2 2 / 2\| 2 |1 + x 2| 1 + x 2 1 + x 2 / 2\ 2 |
| | (1 + x) |(1 + x) 1 + x / 2\ (1 + x)*\1 + x /| |(1 + x) (1 + x)*\1 + x / / 2\ / 2\ (1 + x) *\1 + x / / 2\ | (1 + x) 1 + x 1 + x (1 + x) 1 + x / 2\ / 2\ (1 + x)*\1 + x / / 2\ (1 + x)*\1 + x / 1 + x 1 + x / 2\ (1 + x) *\1 + x / / 2\ (1 + x)*\1 + x / | (1 + x) |(1 + x) 1 + x / 2\ (1 + x)*\1 + x /| 1 + x \ 1 + x / / 2\ 1 + x (1 + x)*\1 + x / 1 + x |
\ \ \ \1 + x / / \ \1 + x / \1 + x / (1 + x)*\1 + x / / \1 + x / \1 + x / \1 + x / \1 + x / (1 + x)*\1 + x / / \ \1 + x / / \1 + x / /
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
2
2 / 2\
(1 + x) *\1 + x /
$$\frac{2 \left(- \frac{24 x^{2} \left(x^{2} + 2 x \left(x + 1\right) + 1\right)}{\left(x^{2} + 1\right)^{2}} + \frac{24 x \left(3 x + 1\right)}{x^{2} + 1} + x \left(\frac{48 x^{3} \left(x^{2} + 2 x \left(x + 1\right) + 1\right)}{\left(x^{2} + 1\right)^{3}} - \frac{48 x^{2} \left(3 x + 1\right)}{\left(x^{2} + 1\right)^{2}} + \frac{4 x^{2} \left(\frac{2 x}{x^{2} + 1} + \frac{1}{x + 1}\right) \left(x^{2} + 2 x \left(x + 1\right) + 1\right)}{\left(x^{2} + 1\right)^{2}} + \frac{36 x^{2} \left(x^{2} + 2 x \left(x + 1\right) + 1\right)}{\left(x + 1\right) \left(x^{2} + 1\right)^{2}} - \frac{4 x \left(3 x + 1\right) \left(\frac{2 x}{x^{2} + 1} + \frac{1}{x + 1}\right)}{x^{2} + 1} + \frac{4 x \left(x^{2} + 2 x \left(x + 1\right) + 1\right) \left(\frac{4 x^{2}}{\left(x^{2} + 1\right)^{2}} + \frac{2 x}{\left(x + 1\right) \left(x^{2} + 1\right)} - \frac{1}{x^{2} + 1} + \frac{1}{\left(x + 1\right)^{2}}\right)}{x^{2} + 1} + \frac{36 x}{x^{2} + 1} - \frac{18 x \left(x^{2} + 2 x \left(x + 1\right) + 1\right)}{\left(x^{2} + 1\right)^{2}} - \frac{32 x \left(3 x + 1\right)}{\left(x + 1\right) \left(x^{2} + 1\right)} + \frac{2 x \left(\frac{2 x}{x^{2} + 1} + \frac{1}{x + 1}\right) \left(x^{2} + 2 x \left(x + 1\right) + 1\right)}{\left(x + 1\right) \left(x^{2} + 1\right)} + \frac{18 x \left(x^{2} + 2 x \left(x + 1\right) + 1\right)}{\left(x + 1\right)^{2} \left(x^{2} + 1\right)} - 4 \left(3 x + 1\right) \left(\frac{4 x^{2}}{\left(x^{2} + 1\right)^{2}} + \frac{2 x}{\left(x + 1\right) \left(x^{2} + 1\right)} - \frac{1}{x^{2} + 1} + \frac{1}{\left(x + 1\right)^{2}}\right) + \frac{8 \left(3 x + 1\right)}{x^{2} + 1} + 3 \left(x^{2} + 2 x \left(x + 1\right) + 1\right) \left(\frac{8 x^{3}}{\left(x^{2} + 1\right)^{3}} + \frac{4 x^{2}}{\left(x + 1\right) \left(x^{2} + 1\right)^{2}} - \frac{4 x}{\left(x^{2} + 1\right)^{2}} + \frac{2 x}{\left(x + 1\right)^{2} \left(x^{2} + 1\right)} - \frac{1}{\left(x + 1\right) \left(x^{2} + 1\right)} + \frac{1}{\left(x + 1\right)^{3}}\right) - \frac{\left(\frac{2 x}{x^{2} + 1} + \frac{1}{x + 1}\right) \left(x^{2} + 2 x \left(x + 1\right) + 1\right)}{x^{2} + 1} - \frac{2 \left(3 x + 1\right) \left(\frac{2 x}{x^{2} + 1} + \frac{1}{x + 1}\right)}{x + 1} + \frac{2 \left(x^{2} + 2 x \left(x + 1\right) + 1\right) \left(\frac{4 x^{2}}{\left(x^{2} + 1\right)^{2}} + \frac{2 x}{\left(x + 1\right) \left(x^{2} + 1\right)} - \frac{1}{x^{2} + 1} + \frac{1}{\left(x + 1\right)^{2}}\right)}{x + 1} + \frac{18}{x + 1} - \frac{6 \left(x^{2} + 2 x \left(x + 1\right) + 1\right)}{\left(x + 1\right) \left(x^{2} + 1\right)} - \frac{12 \left(3 x + 1\right)}{\left(x + 1\right)^{2}} + \frac{\left(\frac{2 x}{x^{2} + 1} + \frac{1}{x + 1}\right) \left(x^{2} + 2 x \left(x + 1\right) + 1\right)}{\left(x + 1\right)^{2}} + \frac{6 \left(x^{2} + 2 x \left(x + 1\right) + 1\right)}{\left(x + 1\right)^{3}}\right) - \frac{4 x \left(\frac{2 x}{x^{2} + 1} + \frac{1}{x + 1}\right) \left(x^{2} + 2 x \left(x + 1\right) + 1\right)}{x^{2} + 1} - \frac{16 x \left(x^{2} + 2 x \left(x + 1\right) + 1\right)}{\left(x + 1\right) \left(x^{2} + 1\right)} + 4 \left(3 x + 1\right) \left(\frac{2 x}{x^{2} + 1} + \frac{1}{x + 1}\right) - 4 \left(x^{2} + 2 x \left(x + 1\right) + 1\right) \left(\frac{4 x^{2}}{\left(x^{2} + 1\right)^{2}} + \frac{2 x}{\left(x + 1\right) \left(x^{2} + 1\right)} - \frac{1}{x^{2} + 1} + \frac{1}{\left(x + 1\right)^{2}}\right) - 12 + \frac{4 \left(x^{2} + 2 x \left(x + 1\right) + 1\right)}{x^{2} + 1} + \frac{12 \left(3 x + 1\right)}{x + 1} - \frac{2 \left(\frac{2 x}{x^{2} + 1} + \frac{1}{x + 1}\right) \left(x^{2} + 2 x \left(x + 1\right) + 1\right)}{x + 1} - \frac{6 \left(x^{2} + 2 x \left(x + 1\right) + 1\right)}{\left(x + 1\right)^{2}}\right)}{\left(x + 1\right)^{2} \left(x^{2} + 1\right)^{2}}$$
Tercera derivada
[src]
/ / 1 2*x \ / 2 \ / 1 2*x \ / 2 \ \
| |----- + ------|*\1 + x + 2*x*(1 + x)/ 2*x*|----- + ------|*\1 + x + 2*x*(1 + x)/ |
| / 2 \ / 2 \ / 2 \ |1 + x 2| 2 / 2 \ |1 + x 2| / 2 \| / 2 \ / 2 \
| 6*(1 + 3*x) 2*\1 + x + 2*x*(1 + x)/ / 1 2*x \ / 2 \ | 1 1 4*x 2*x | 3*\1 + x + 2*x*(1 + x)/ \ 1 + x / 12*x*(1 + 3*x) 12*x *\1 + x + 2*x*(1 + x)/ \ 1 + x / 8*x*\1 + x + 2*x*(1 + x)/| 3*\1 + x + 2*x*(1 + x)/ / 1 2*x \ / 2 \ 6*x*\1 + x + 2*x*(1 + x)/
-6 - 18*x - x*|6 - ----------- - ------------------------ - 2*(1 + 3*x)*|----- + ------| + 2*\1 + x + 2*x*(1 + x)/*|-------- - ------ + --------- + ----------------| + ------------------------ + --------------------------------------- - -------------- + ---------------------------- + ------------------------------------------- + --------------------------| + ------------------------ + 3*|----- + ------|*\1 + x + 2*x*(1 + x)/ + --------------------------
| 1 + x 2 |1 + x 2| | 2 2 2 / 2\| 2 1 + x 2 2 2 / 2\ | 1 + x |1 + x 2| 2
| 1 + x \ 1 + x / |(1 + x) 1 + x / 2\ (1 + x)*\1 + x /| (1 + x) 1 + x / 2\ 1 + x (1 + x)*\1 + x / | \ 1 + x / 1 + x
\ \ \1 + x / / \1 + x / /
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
2
2 / 2\
(1 + x) *\1 + x /
$$\frac{- x \left(\frac{12 x^{2} \left(x^{2} + 2 x \left(x + 1\right) + 1\right)}{\left(x^{2} + 1\right)^{2}} - \frac{12 x \left(3 x + 1\right)}{x^{2} + 1} + \frac{2 x \left(\frac{2 x}{x^{2} + 1} + \frac{1}{x + 1}\right) \left(x^{2} + 2 x \left(x + 1\right) + 1\right)}{x^{2} + 1} + \frac{8 x \left(x^{2} + 2 x \left(x + 1\right) + 1\right)}{\left(x + 1\right) \left(x^{2} + 1\right)} - 2 \left(3 x + 1\right) \left(\frac{2 x}{x^{2} + 1} + \frac{1}{x + 1}\right) + 2 \left(x^{2} + 2 x \left(x + 1\right) + 1\right) \left(\frac{4 x^{2}}{\left(x^{2} + 1\right)^{2}} + \frac{2 x}{\left(x + 1\right) \left(x^{2} + 1\right)} - \frac{1}{x^{2} + 1} + \frac{1}{\left(x + 1\right)^{2}}\right) + 6 - \frac{2 \left(x^{2} + 2 x \left(x + 1\right) + 1\right)}{x^{2} + 1} - \frac{6 \left(3 x + 1\right)}{x + 1} + \frac{\left(\frac{2 x}{x^{2} + 1} + \frac{1}{x + 1}\right) \left(x^{2} + 2 x \left(x + 1\right) + 1\right)}{x + 1} + \frac{3 \left(x^{2} + 2 x \left(x + 1\right) + 1\right)}{\left(x + 1\right)^{2}}\right) - 18 x + \frac{6 x \left(x^{2} + 2 x \left(x + 1\right) + 1\right)}{x^{2} + 1} + 3 \left(\frac{2 x}{x^{2} + 1} + \frac{1}{x + 1}\right) \left(x^{2} + 2 x \left(x + 1\right) + 1\right) - 6 + \frac{3 \left(x^{2} + 2 x \left(x + 1\right) + 1\right)}{x + 1}}{\left(x + 1\right)^{2} \left(x^{2} + 1\right)^{2}}$$
Gráfico