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
- x+ln(|x+ tres |/(x- dos))
- x más ln( módulo de x más 3| dividir por (x menos 2))
- x más ln( módulo de x más tres | dividir por (x menos dos))
- x+ln|x+3|/x-2
- x+ln(|x+3| dividir por (x-2))
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Expresiones semejantes
- x+ln(|x-3|/(x-2))
- x-ln(|x+3|/(x-2))
- x+ln(|x+3|/(x+2))
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Expresiones con funciones
- ln
- ln(×)
- ln(x+a)
- ln(e^x-e^a)
- ln^3(3x)
- ln(2/x)
- Módulo |
- |x|:x
- |x|((x^2)-pi^2)^2
- ||x|-|x-11||
- |x-t|
- |x|/sin(x)*cos(x)
Derivada de x+ln(|x+3|/(x-2))
Solución
Ha introducido
[src]
/|x + 3|\
x + log|-------|
\ x - 2 /
$$x + \log{\left(\frac{\left|{x + 3}\right|}{x - 2} \right)}$$
x + log(|x + 3|/(x - 2))
Primera derivada
[src]
/sign(3 + x) |x + 3| \
(x - 2)*|----------- - --------|
| x - 2 2|
\ (x - 2) /
1 + --------------------------------
|x + 3|
$$\frac{\left(x - 2\right) \left(\frac{\operatorname{sign}{\left(x + 3 \right)}}{x - 2} - \frac{\left|{x + 3}\right|}{\left(x - 2\right)^{2}}\right)}{\left|{x + 3}\right|} + 1$$
Segunda derivada
[src]
/ |3 + x| sign(3 + x) \
2*|--------- - ----------- + DiracDelta(3 + x)| |3 + x| / |3 + x| \
| 2 -2 + x | - ------- + sign(3 + x) |- ------- + sign(3 + x)|*sign(3 + x)
\(-2 + x) / -2 + x \ -2 + x /
----------------------------------------------- + ----------------------- - -------------------------------------
|3 + x| (-2 + x)*|3 + x| 2
(3 + x)
$$\frac{2 \left(\delta\left(x + 3\right) - \frac{\operatorname{sign}{\left(x + 3 \right)}}{x - 2} + \frac{\left|{x + 3}\right|}{\left(x - 2\right)^{2}}\right)}{\left|{x + 3}\right|} - \frac{\left(\operatorname{sign}{\left(x + 3 \right)} - \frac{\left|{x + 3}\right|}{x - 2}\right) \operatorname{sign}{\left(x + 3 \right)}}{\left(x + 3\right)^{2}} + \frac{\operatorname{sign}{\left(x + 3 \right)} - \frac{\left|{x + 3}\right|}{x - 2}}{\left(x - 2\right) \left|{x + 3}\right|}$$
Tercera derivada
[src]
/ 3*DiracDelta(3 + x) 3*|3 + x| 3*sign(3 + x) / |3 + x| sign(3 + x) \ / |3 + x| sign(3 + x) \ \ |- ------------------- - --------- + ------------- + DiracDelta(3 + x, 1) / |3 + x| \ / |3 + x| \ 2*|--------- - ----------- + DiracDelta(3 + x)|*sign(3 + x) 2*|--------- - ----------- + DiracDelta(3 + x)| / |3 + x| \ | | -2 + x 3 2 |- ------- + sign(3 + x)|*sign(3 + x) |- ------- + sign(3 + x)|*DiracDelta(3 + x) | 2 -2 + x | | 2 -2 + x | |- ------- + sign(3 + x)|*sign(3 + x)| | (-2 + x) (-2 + x) \ -2 + x / \ -2 + x / \(-2 + x) / \(-2 + x) / \ -2 + x / | 2*|------------------------------------------------------------------------ + ------------------------------------- - ------------------------------------------- - ----------------------------------------------------------- + ----------------------------------------------- - -------------------------------------| | |3 + x| 3 2 2 (-2 + x)*|3 + x| 2 | \ (3 + x) (3 + x) (3 + x) (-2 + x)*(3 + x) /
$$2 \left(\frac{\delta^{\left( 1 \right)}\left( x + 3 \right) - \frac{3 \delta\left(x + 3\right)}{x - 2} + \frac{3 \operatorname{sign}{\left(x + 3 \right)}}{\left(x - 2\right)^{2}} - \frac{3 \left|{x + 3}\right|}{\left(x - 2\right)^{3}}}{\left|{x + 3}\right|} - \frac{\left(\operatorname{sign}{\left(x + 3 \right)} - \frac{\left|{x + 3}\right|}{x - 2}\right) \delta\left(x + 3\right)}{\left(x + 3\right)^{2}} - \frac{2 \left(\delta\left(x + 3\right) - \frac{\operatorname{sign}{\left(x + 3 \right)}}{x - 2} + \frac{\left|{x + 3}\right|}{\left(x - 2\right)^{2}}\right) \operatorname{sign}{\left(x + 3 \right)}}{\left(x + 3\right)^{2}} + \frac{\left(\operatorname{sign}{\left(x + 3 \right)} - \frac{\left|{x + 3}\right|}{x - 2}\right) \operatorname{sign}{\left(x + 3 \right)}}{\left(x + 3\right)^{3}} + \frac{2 \left(\delta\left(x + 3\right) - \frac{\operatorname{sign}{\left(x + 3 \right)}}{x - 2} + \frac{\left|{x + 3}\right|}{\left(x - 2\right)^{2}}\right)}{\left(x - 2\right) \left|{x + 3}\right|} - \frac{\left(\operatorname{sign}{\left(x + 3 \right)} - \frac{\left|{x + 3}\right|}{x - 2}\right) \operatorname{sign}{\left(x + 3 \right)}}{\left(x - 2\right) \left(x + 3\right)^{2}}\right)$$