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 y=5x-2
-
Derivada de 2^(5*x)
-
Derivada de (t^(2)+1)÷(t^(1÷2)-1)
-
Derivada de (sqrt(x)-1)/(sqrt(x)*2-x-1)
-
Expresiones idénticas
- y=(x+lnx)^(uno /x)
- y es igual a (x más lnx) en el grado (1 dividir por x)
- y es igual a (x más lnx) en el grado (uno dividir por x)
- y=(x+lnx)(1/x)
- y=x+lnx1/x
- y=x+lnx^1/x
- y=(x+lnx)^(1 dividir por x)
-
Expresiones semejantes
- y=(x-lnx)^(1/x)
- y=(x+lnx)^(1/x)p(-x)
-
Expresiones con funciones
- ln
- ln(x+a)
- ln*(sqrt(1+e^x)-1)-ln*(sqrt(1+e^x)+1)
- ln(3×^2+7×)
- ln(×)
- ln(1+e^-x)
Derivada de y=(x+lnx)^(1/x)
Solución
Ha introducido
[src]
x ____________ \/ x + log(x)
$$\left(x + \log{\left(x \right)}\right)^{\frac{1}{x}}$$
(x + log(x))^(1/x)
Solución detallada
-
No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Respuesta:
Primera derivada
[src]
/ 1 \
| 1 + - |
x ____________ | log(x + log(x)) x |
\/ x + log(x) *|- --------------- + --------------|
| 2 x*(x + log(x))|
\ x /
$$\left(x + \log{\left(x \right)}\right)^{\frac{1}{x}} \left(\frac{1 + \frac{1}{x}}{x \left(x + \log{\left(x \right)}\right)} - \frac{\log{\left(x + \log{\left(x \right)} \right)}}{x^{2}}\right)$$
Segunda derivada
[src]
/ 2 \
|/ 1 \ |
|| 1 + - | 2 |
|| x log(x + log(x))| / 1\ / 1\ |
||---------- - ---------------| |1 + -| 2*|1 + -| |
x ____________ |\x + log(x) x / 1 \ x/ 2*log(x + log(x)) \ x/ |
\/ x + log(x) *|------------------------------- - --------------- - ------------- + ----------------- - --------------|
| x 2 2 2 x*(x + log(x))|
\ x *(x + log(x)) (x + log(x)) x /
-----------------------------------------------------------------------------------------------------------------------
x
$$\frac{\left(x + \log{\left(x \right)}\right)^{\frac{1}{x}} \left(- \frac{\left(1 + \frac{1}{x}\right)^{2}}{\left(x + \log{\left(x \right)}\right)^{2}} - \frac{2 \left(1 + \frac{1}{x}\right)}{x \left(x + \log{\left(x \right)}\right)} + \frac{\left(\frac{1 + \frac{1}{x}}{x + \log{\left(x \right)}} - \frac{\log{\left(x + \log{\left(x \right)} \right)}}{x}\right)^{2}}{x} + \frac{2 \log{\left(x + \log{\left(x \right)} \right)}}{x^{2}} - \frac{1}{x^{2} \left(x + \log{\left(x \right)}\right)}\right)}{x}$$
Tercera derivada
[src]
/ / 2 \ \
| 3 / 1 \ | / 1\ / 1\ | |
|/ 1 \ | 1 + - | | |1 + -| 2*|1 + -| | |
|| 1 + - | 3 | x log(x + log(x))| | 1 \ x/ 2*log(x + log(x)) \ x/ | 2 |
|| x log(x + log(x))| / 1\ 3*|---------- - ---------------|*|--------------- + ------------- - ----------------- + --------------| / 1\ / 1\ / 1\ |
||---------- - ---------------| 2*|1 + -| \x + log(x) x / | 2 2 2 x*(x + log(x))| 3*|1 + -| 3*|1 + -| 6*|1 + -| |
x ____________ |\x + log(x) x / 6*log(x + log(x)) \ x/ 5 \x *(x + log(x)) (x + log(x)) x / \ x/ \ x/ \ x/ |
\/ x + log(x) *|------------------------------- - ----------------- + ------------- + --------------- - ------------------------------------------------------------------------------------------------------- + --------------- + ---------------- + ---------------|
| 2 3 3 3 x 2 2 2 2 |
\ x x (x + log(x)) x *(x + log(x)) x*(x + log(x)) x *(x + log(x)) x *(x + log(x))/
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
x
$$\frac{\left(x + \log{\left(x \right)}\right)^{\frac{1}{x}} \left(\frac{2 \left(1 + \frac{1}{x}\right)^{3}}{\left(x + \log{\left(x \right)}\right)^{3}} + \frac{3 \left(1 + \frac{1}{x}\right)^{2}}{x \left(x + \log{\left(x \right)}\right)^{2}} - \frac{3 \left(\frac{1 + \frac{1}{x}}{x + \log{\left(x \right)}} - \frac{\log{\left(x + \log{\left(x \right)} \right)}}{x}\right) \left(\frac{\left(1 + \frac{1}{x}\right)^{2}}{\left(x + \log{\left(x \right)}\right)^{2}} + \frac{2 \left(1 + \frac{1}{x}\right)}{x \left(x + \log{\left(x \right)}\right)} - \frac{2 \log{\left(x + \log{\left(x \right)} \right)}}{x^{2}} + \frac{1}{x^{2} \left(x + \log{\left(x \right)}\right)}\right)}{x} + \frac{6 \left(1 + \frac{1}{x}\right)}{x^{2} \left(x + \log{\left(x \right)}\right)} + \frac{3 \left(1 + \frac{1}{x}\right)}{x^{2} \left(x + \log{\left(x \right)}\right)^{2}} + \frac{\left(\frac{1 + \frac{1}{x}}{x + \log{\left(x \right)}} - \frac{\log{\left(x + \log{\left(x \right)} \right)}}{x}\right)^{3}}{x^{2}} - \frac{6 \log{\left(x + \log{\left(x \right)} \right)}}{x^{3}} + \frac{5}{x^{3} \left(x + \log{\left(x \right)}\right)}\right)}{x}$$
Gráfico