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+3)
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Derivada de 4*y
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Derivada de (2x-7)^8
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Derivada de (-1)/x-3*x
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Expresiones idénticas
- x/((x+ uno)(x- dos))
- x dividir por ((x más 1)(x menos 2))
- x dividir por ((x más uno)(x menos dos))
- x/x+1x-2
- x dividir por ((x+1)(x-2))
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Expresiones semejantes
- x/((x-1)(x-2))
- (x/(x+1))^(x-2)
- x/((x+1)(x+2))
Derivada de x/((x+1)(x-2))
Solución
Ha introducido
[src]
x --------------- (x + 1)*(x - 2)
$$\frac{x}{\left(x - 2\right) \left(x + 1\right)}$$
x/(((x + 1)*(x - 2)))
Solución detallada
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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:
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; 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:
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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]
1 x*(1 - 2*x)
--------------- + -----------------
(x + 1)*(x - 2) 2 2
(x + 1) *(x - 2)
$$\frac{x \left(1 - 2 x\right)}{\left(x - 2\right)^{2} \left(x + 1\right)^{2}} + \frac{1}{\left(x - 2\right) \left(x + 1\right)}$$
Segunda derivada
[src]
/ -1 + 2*x -1 + 2*x / 1 1 \\
2 - 4*x + x*|-2 + -------- + -------- + (-1 + 2*x)*|----- + ------||
\ 1 + x -2 + x \1 + x -2 + x//
--------------------------------------------------------------------
2 2
(1 + x) *(-2 + x)
$$\frac{x \left(\left(2 x - 1\right) \left(\frac{1}{x + 1} + \frac{1}{x - 2}\right) - 2 + \frac{2 x - 1}{x + 1} + \frac{2 x - 1}{x - 2}\right) - 4 x + 2}{\left(x - 2\right)^{2} \left(x + 1\right)^{2}}$$
Tercera derivada
[src]
/ / 1 1 \ / 1 1 \ \
| (-1 + 2*x)*|----- + ------| (-1 + 2*x)*|----- + ------| |
| 8 8 / 1 1 1 \ 3*(-1 + 2*x) 3*(-1 + 2*x) \1 + x -2 + x/ \1 + x -2 + x/ 4*(-1 + 2*x) | 3*(-1 + 2*x) 3*(-1 + 2*x) / 1 1 \
-6 - x*|- ----- - ------ + 2*(-1 + 2*x)*|-------- + --------- + ----------------| + ------------ + ------------ + --------------------------- + --------------------------- + ----------------| + ------------ + ------------ + 3*(-1 + 2*x)*|----- + ------|
| 1 + x -2 + x | 2 2 (1 + x)*(-2 + x)| 2 2 1 + x -2 + x (1 + x)*(-2 + x)| 1 + x -2 + x \1 + x -2 + x/
\ \(1 + x) (-2 + x) / (1 + x) (-2 + x) /
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2 2
(1 + x) *(-2 + x)
$$\frac{- x \left(2 \left(2 x - 1\right) \left(\frac{1}{\left(x + 1\right)^{2}} + \frac{1}{\left(x - 2\right) \left(x + 1\right)} + \frac{1}{\left(x - 2\right)^{2}}\right) + \frac{\left(2 x - 1\right) \left(\frac{1}{x + 1} + \frac{1}{x - 2}\right)}{x + 1} - \frac{8}{x + 1} + \frac{3 \left(2 x - 1\right)}{\left(x + 1\right)^{2}} + \frac{\left(2 x - 1\right) \left(\frac{1}{x + 1} + \frac{1}{x - 2}\right)}{x - 2} - \frac{8}{x - 2} + \frac{4 \left(2 x - 1\right)}{\left(x - 2\right) \left(x + 1\right)} + \frac{3 \left(2 x - 1\right)}{\left(x - 2\right)^{2}}\right) + 3 \left(2 x - 1\right) \left(\frac{1}{x + 1} + \frac{1}{x - 2}\right) - 6 + \frac{3 \left(2 x - 1\right)}{x + 1} + \frac{3 \left(2 x - 1\right)}{x - 2}}{\left(x - 2\right)^{2} \left(x + 1\right)^{2}}$$
5-я производная
[src]
/ / / 1 1 1 \ / 1 1 1 \ / 1 1 1 \ / 1 1 1 \ / 1 1 1 1 \ / 1 1 1 1 \ / 1 1 1 \\ / 1 1 1 \ / 1 1 1 \ \
| / 1 1 \ / 1 1 \ | 4*|-------- + --------- + ----------------| 4*|-------- + --------- + ----------------| / 1 1 \ / 1 1 \ / 1 1 \ / 1 1 \ / 1 1 \ 2*(-1 + 2*x)*|-------- + --------- + ----------------| 2*(-1 + 2*x)*|-------- + --------- + ----------------| 3*(-1 + 2*x)*|-------- + --------- + ----------------- + -----------------| 3*(-1 + 2*x)*|-------- + --------- + ----------------- + -----------------| / 1 1 \ / 1 1 \ 2*(-1 + 2*x)*|-------- + --------- + ----------------|| / 1 1 \ / 1 1 \ 10*(-1 + 2*x)*|-------- + --------- + ----------------| 10*(-1 + 2*x)*|-------- + --------- + ----------------| / 1 1 \|
| 10*|----- + ------| 10*|----- + ------| | | 2 2 (1 + x)*(-2 + x)| | 2 2 (1 + x)*(-2 + x)| 2*|----- + ------| 2*|----- + ------| (-1 + 2*x)*|----- + ------| (-1 + 2*x)*|----- + ------| 2*|----- + ------| | 2 2 (1 + x)*(-2 + x)| | 2 2 (1 + x)*(-2 + x)| | 3 3 2 2 | | 3 3 2 2 | (-1 + 2*x)*|----- + ------| (-1 + 2*x)*|----- + ------| | 2 2 (1 + x)*(-2 + x)|| 5*(-1 + 2*x)*|----- + ------| 5*(-1 + 2*x)*|----- + ------| | 2 2 (1 + x)*(-2 + x)| | 2 2 (1 + x)*(-2 + x)| 5*(-1 + 2*x)*|----- + ------||
| 80 80 100 \1 + x -2 + x/ \1 + x -2 + x/ | 26 26 36 36 \(1 + x) (-2 + x) / \(1 + x) (-2 + x) / \1 + x -2 + x/ \1 + x -2 + x/ / 1 1 1 1 1 \ 10*(-1 + 2*x) 10*(-1 + 2*x) \1 + x -2 + x/ \1 + x -2 + x/ \1 + x -2 + x/ \(1 + x) (-2 + x) / \(1 + x) (-2 + x) / \(1 + x) (-2 + x) (1 + x)*(-2 + x) (1 + x) *(-2 + x)/ \(1 + x) (-2 + x) (1 + x)*(-2 + x) (1 + x) *(-2 + x)/ 16*(-1 + 2*x) 16*(-1 + 2*x) 18*(-1 + 2*x) \1 + x -2 + x/ \1 + x -2 + x/ \(1 + x) (-2 + x) /| / 1 1 1 1 \ 30*(-1 + 2*x) 30*(-1 + 2*x) \1 + x -2 + x/ \1 + x -2 + x/ \(1 + x) (-2 + x) / \(1 + x) (-2 + x) / 45*(-1 + 2*x) 45*(-1 + 2*x) \1 + x -2 + x/|
2*|- -------- - --------- - ---------------- - ------------------- - ------------------- - 3*x*|- -------- - --------- - ----------------- - ----------------- - ------------------------------------------- - ------------------------------------------- - ------------------ - ------------------ + 4*(-1 + 2*x)*|-------- + --------- + ----------------- + ----------------- + ------------------| + ------------- + ------------- + --------------------------- + --------------------------- - ------------------ + ------------------------------------------------------ + ------------------------------------------------------ + --------------------------------------------------------------------------- + --------------------------------------------------------------------------- + ----------------- + ----------------- + ------------------ + --------------------------- + --------------------------- + ------------------------------------------------------| + 15*(-1 + 2*x)*|-------- + --------- + ----------------- + -----------------| + ------------- + ------------- + ----------------------------- + ----------------------------- + ------------------------------------------------------- + ------------------------------------------------------- + ----------------- + ----------------- + -----------------------------|
| 2 2 (1 + x)*(-2 + x) 1 + x -2 + x | 3 3 2 2 1 + x -2 + x 2 2 | 4 4 3 3 2 2| 4 4 3 3 (1 + x)*(-2 + x) 2 2 1 + x -2 + x 3 3 2 2 2 2 (1 + x)*(-2 + x) | | 3 3 2 2 | 3 3 2 2 1 + x -2 + x 2 2 (1 + x)*(-2 + x) |
\ (1 + x) (-2 + x) \ (1 + x) (-2 + x) (1 + x)*(-2 + x) (1 + x) *(-2 + x) (1 + x) (-2 + x) \(1 + x) (-2 + x) (1 + x)*(-2 + x) (1 + x) *(-2 + x) (1 + x) *(-2 + x) / (1 + x) (-2 + x) (1 + x) (-2 + x) (1 + x) (-2 + x) (1 + x)*(-2 + x) (1 + x) *(-2 + x) (1 + x) *(-2 + x) (1 + x)*(-2 + x) (1 + x) *(-2 + x) / \(1 + x) (-2 + x) (1 + x)*(-2 + x) (1 + x) *(-2 + x)/ (1 + x) (-2 + x) (1 + x) (-2 + x) (1 + x)*(-2 + x) (1 + x) *(-2 + x) /
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2 2
(1 + x) *(-2 + x)
$$\frac{2 \left(- 3 x \left(4 \left(2 x - 1\right) \left(\frac{1}{\left(x + 1\right)^{4}} + \frac{1}{\left(x - 2\right) \left(x + 1\right)^{3}} + \frac{1}{\left(x - 2\right)^{2} \left(x + 1\right)^{2}} + \frac{1}{\left(x - 2\right)^{3} \left(x + 1\right)} + \frac{1}{\left(x - 2\right)^{4}}\right) + \frac{3 \left(2 x - 1\right) \left(\frac{1}{\left(x + 1\right)^{3}} + \frac{1}{\left(x - 2\right) \left(x + 1\right)^{2}} + \frac{1}{\left(x - 2\right)^{2} \left(x + 1\right)} + \frac{1}{\left(x - 2\right)^{3}}\right)}{x + 1} - \frac{4 \left(\frac{1}{\left(x + 1\right)^{2}} + \frac{1}{\left(x - 2\right) \left(x + 1\right)} + \frac{1}{\left(x - 2\right)^{2}}\right)}{x + 1} + \frac{2 \left(2 x - 1\right) \left(\frac{1}{\left(x + 1\right)^{2}} + \frac{1}{\left(x - 2\right) \left(x + 1\right)} + \frac{1}{\left(x - 2\right)^{2}}\right)}{\left(x + 1\right)^{2}} - \frac{2 \left(\frac{1}{x + 1} + \frac{1}{x - 2}\right)}{\left(x + 1\right)^{2}} + \frac{\left(2 x - 1\right) \left(\frac{1}{x + 1} + \frac{1}{x - 2}\right)}{\left(x + 1\right)^{3}} - \frac{26}{\left(x + 1\right)^{3}} + \frac{10 \left(2 x - 1\right)}{\left(x + 1\right)^{4}} + \frac{3 \left(2 x - 1\right) \left(\frac{1}{\left(x + 1\right)^{3}} + \frac{1}{\left(x - 2\right) \left(x + 1\right)^{2}} + \frac{1}{\left(x - 2\right)^{2} \left(x + 1\right)} + \frac{1}{\left(x - 2\right)^{3}}\right)}{x - 2} - \frac{4 \left(\frac{1}{\left(x + 1\right)^{2}} + \frac{1}{\left(x - 2\right) \left(x + 1\right)} + \frac{1}{\left(x - 2\right)^{2}}\right)}{x - 2} + \frac{2 \left(2 x - 1\right) \left(\frac{1}{\left(x + 1\right)^{2}} + \frac{1}{\left(x - 2\right) \left(x + 1\right)} + \frac{1}{\left(x - 2\right)^{2}}\right)}{\left(x - 2\right) \left(x + 1\right)} - \frac{2 \left(\frac{1}{x + 1} + \frac{1}{x - 2}\right)}{\left(x - 2\right) \left(x + 1\right)} + \frac{\left(2 x - 1\right) \left(\frac{1}{x + 1} + \frac{1}{x - 2}\right)}{\left(x - 2\right) \left(x + 1\right)^{2}} - \frac{36}{\left(x - 2\right) \left(x + 1\right)^{2}} + \frac{16 \left(2 x - 1\right)}{\left(x - 2\right) \left(x + 1\right)^{3}} + \frac{2 \left(2 x - 1\right) \left(\frac{1}{\left(x + 1\right)^{2}} + \frac{1}{\left(x - 2\right) \left(x + 1\right)} + \frac{1}{\left(x - 2\right)^{2}}\right)}{\left(x - 2\right)^{2}} - \frac{2 \left(\frac{1}{x + 1} + \frac{1}{x - 2}\right)}{\left(x - 2\right)^{2}} + \frac{\left(2 x - 1\right) \left(\frac{1}{x + 1} + \frac{1}{x - 2}\right)}{\left(x - 2\right)^{2} \left(x + 1\right)} - \frac{36}{\left(x - 2\right)^{2} \left(x + 1\right)} + \frac{18 \left(2 x - 1\right)}{\left(x - 2\right)^{2} \left(x + 1\right)^{2}} + \frac{\left(2 x - 1\right) \left(\frac{1}{x + 1} + \frac{1}{x - 2}\right)}{\left(x - 2\right)^{3}} - \frac{26}{\left(x - 2\right)^{3}} + \frac{16 \left(2 x - 1\right)}{\left(x - 2\right)^{3} \left(x + 1\right)} + \frac{10 \left(2 x - 1\right)}{\left(x - 2\right)^{4}}\right) + 15 \left(2 x - 1\right) \left(\frac{1}{\left(x + 1\right)^{3}} + \frac{1}{\left(x - 2\right) \left(x + 1\right)^{2}} + \frac{1}{\left(x - 2\right)^{2} \left(x + 1\right)} + \frac{1}{\left(x - 2\right)^{3}}\right) + \frac{10 \left(2 x - 1\right) \left(\frac{1}{\left(x + 1\right)^{2}} + \frac{1}{\left(x - 2\right) \left(x + 1\right)} + \frac{1}{\left(x - 2\right)^{2}}\right)}{x + 1} - \frac{10 \left(\frac{1}{x + 1} + \frac{1}{x - 2}\right)}{x + 1} + \frac{5 \left(2 x - 1\right) \left(\frac{1}{x + 1} + \frac{1}{x - 2}\right)}{\left(x + 1\right)^{2}} - \frac{80}{\left(x + 1\right)^{2}} + \frac{30 \left(2 x - 1\right)}{\left(x + 1\right)^{3}} + \frac{10 \left(2 x - 1\right) \left(\frac{1}{\left(x + 1\right)^{2}} + \frac{1}{\left(x - 2\right) \left(x + 1\right)} + \frac{1}{\left(x - 2\right)^{2}}\right)}{x - 2} - \frac{10 \left(\frac{1}{x + 1} + \frac{1}{x - 2}\right)}{x - 2} + \frac{5 \left(2 x - 1\right) \left(\frac{1}{x + 1} + \frac{1}{x - 2}\right)}{\left(x - 2\right) \left(x + 1\right)} - \frac{100}{\left(x - 2\right) \left(x + 1\right)} + \frac{45 \left(2 x - 1\right)}{\left(x - 2\right) \left(x + 1\right)^{2}} + \frac{5 \left(2 x - 1\right) \left(\frac{1}{x + 1} + \frac{1}{x - 2}\right)}{\left(x - 2\right)^{2}} - \frac{80}{\left(x - 2\right)^{2}} + \frac{45 \left(2 x - 1\right)}{\left(x - 2\right)^{2} \left(x + 1\right)} + \frac{30 \left(2 x - 1\right)}{\left(x - 2\right)^{3}}\right)}{\left(x - 2\right)^{2} \left(x + 1\right)^{2}}$$
Gráfico