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 e^x*sin(x)
-
Derivada de x*e^(1/x)
- Derivada de x!
-
Derivada de e^y
-
Expresiones idénticas
- |x|/ln(|x|)
- módulo de x| dividir por ln(|x|)
- |x|/ln|x|
- |x| dividir por ln(|x|)
-
Expresiones semejantes
- (|x|)/(ln|x|)
-
Expresiones con funciones
- ln
- ln(x+√(x²+1))
- ln(x-4)
- ln(x²+2x)
- ln(x^2+2x)
- ln((x+1)÷(x-1))
- Módulo |
- |x+3|
- |x|*x
- |x|*(sin(x))^2
- |z|*z
- |x|^(π)
Derivada de |x|/ln(|x|)
Solución
Ha introducido
[src]
|x| -------- log(|x|)
$$\frac{\left|{x}\right|}{\log{\left(\left|{x}\right| \right)}}$$
|x|/log(|x|)
Primera derivada
[src]
sign(x) sign(x)
-------- - ---------
log(|x|) 2
log (|x|)
$$\frac{\operatorname{sign}{\left(x \right)}}{\log{\left(\left|{x}\right| \right)}} - \frac{\operatorname{sign}{\left(x \right)}}{\log{\left(\left|{x}\right| \right)}^{2}}$$
Segunda derivada
[src]
/ 2 2 \
|sign (x) 2*DiracDelta(x) 2*sign (x)|
|-------- - --------------- + -----------|*|x|
| 2 |x| 2 | 2
\ x x *log(|x|)/ 2*sign (x)
2*DiracDelta(x) + ---------------------------------------------- - ------------
log(|x|) |x|*log(|x|)
-------------------------------------------------------------------------------
log(|x|)
$$\frac{\frac{\left(- \frac{2 \delta\left(x\right)}{\left|{x}\right|} + \frac{\operatorname{sign}^{2}{\left(x \right)}}{x^{2}} + \frac{2 \operatorname{sign}^{2}{\left(x \right)}}{x^{2} \log{\left(\left|{x}\right| \right)}}\right) \left|{x}\right|}{\log{\left(\left|{x}\right| \right)}} + 2 \delta\left(x\right) - \frac{2 \operatorname{sign}^{2}{\left(x \right)}}{\log{\left(\left|{x}\right| \right)} \left|{x}\right|}}{\log{\left(\left|{x}\right| \right)}}$$
Tercera derivada
[src]
/ 2 2 3 3 \ / 2 2 \
|sign (x) DiracDelta(x, 1) 3*DiracDelta(x)*sign(x) 2*sign (x) sign (x) 6*DiracDelta(x)*sign(x) 3*sign (x) | |sign (x) 2*DiracDelta(x) 2*sign (x)|
2*|-------- + ---------------- - ----------------------- + ----------- + --------------- - ----------------------- + ----------------|*|x| 3*|-------- - --------------- + -----------|*sign(x)
| 3 |x| 2 3 2 2 2 2 | | 2 |x| 2 |
\ x x x *log(|x|) x *|x|*log(|x|) x *log(|x|) x *|x|*log (|x|)/ \ x x *log(|x|)/ 6*DiracDelta(x)*sign(x)
2*DiracDelta(x, 1) - ------------------------------------------------------------------------------------------------------------------------------------------ + ---------------------------------------------------- - -----------------------
log(|x|) log(|x|) |x|*log(|x|)
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
log(|x|)
$$\frac{\frac{3 \left(- \frac{2 \delta\left(x\right)}{\left|{x}\right|} + \frac{\operatorname{sign}^{2}{\left(x \right)}}{x^{2}} + \frac{2 \operatorname{sign}^{2}{\left(x \right)}}{x^{2} \log{\left(\left|{x}\right| \right)}}\right) \operatorname{sign}{\left(x \right)}}{\log{\left(\left|{x}\right| \right)}} - \frac{2 \left(\frac{\delta^{\left( 1 \right)}\left( x \right)}{\left|{x}\right|} - \frac{3 \delta\left(x\right) \operatorname{sign}{\left(x \right)}}{x^{2}} - \frac{6 \delta\left(x\right) \operatorname{sign}{\left(x \right)}}{x^{2} \log{\left(\left|{x}\right| \right)}} + \frac{\operatorname{sign}^{3}{\left(x \right)}}{x^{2} \log{\left(\left|{x}\right| \right)} \left|{x}\right|} + \frac{3 \operatorname{sign}^{3}{\left(x \right)}}{x^{2} \log{\left(\left|{x}\right| \right)}^{2} \left|{x}\right|} + \frac{\operatorname{sign}^{2}{\left(x \right)}}{x^{3}} + \frac{2 \operatorname{sign}^{2}{\left(x \right)}}{x^{3} \log{\left(\left|{x}\right| \right)}}\right) \left|{x}\right|}{\log{\left(\left|{x}\right| \right)}} + 2 \delta^{\left( 1 \right)}\left( x \right) - \frac{6 \delta\left(x\right) \operatorname{sign}{\left(x \right)}}{\log{\left(\left|{x}\right| \right)} \left|{x}\right|}}{\log{\left(\left|{x}\right| \right)}}$$
Gráfico