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*cos(3*x)
-
Derivada de x^(7/6)
-
Derivada de (x^2)/4
-
Derivada de t
-
Expresiones idénticas
- x^x*(ln(uno +x^x))/(uno +x^x)
- x en el grado x multiplicar por (ln(1 más x en el grado x)) dividir por (1 más x en el grado x)
- x en el grado x multiplicar por (ln(uno más x en el grado x)) dividir por (uno más x en el grado x)
- xx*(ln(1+xx))/(1+xx)
- xx*ln1+xx/1+xx
- x^x(ln(1+x^x))/(1+x^x)
- xx(ln(1+xx))/(1+xx)
- xxln1+xx/1+xx
- x^xln1+x^x/1+x^x
- x^x*(ln(1+x^x)) dividir por (1+x^x)
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Expresiones semejantes
- x^x*(ln(1-x^x))/(1+x^x)
- x^x*(ln(1+x^x))/(1-x^x)
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Expresiones con funciones
- ln
- ln(x+k)
- ln4x
- ln(3/x)
- ln√(x-1)
- ln(16+9x^2)
Derivada de x^x*(ln(1+x^x))/(1+x^x)
Solución
Ha introducido
[src]
x / x\
x *log\1 + x /
--------------
x
1 + x
$$\frac{x^{x} \log{\left(x^{x} + 1 \right)}}{x^{x} + 1}$$
(x^x*log(1 + x^x))/(1 + x^x)
Solución detallada
-
Se aplica la regla de la derivada parcial:
y .
Para calcular :
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Se aplica la regla de la derivada de una multiplicación:
; calculamos :
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
; calculamos :
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Sustituimos .
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Derivado es .
-
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Luego se aplica una cadena de reglas. Multiplicamos por :
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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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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Como resultado de:
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Como resultado de la secuencia de reglas:
-
Como resultado de:
-
Para calcular :
-
diferenciamos miembro por miembro:
-
La derivada de una constante es igual a cero.
-
No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Como resultado de:
-
Ahora aplicamos la regla de la derivada de una divesión:
Simplificamos:
Respuesta:
Primera derivada
[src]
2*x
x / x\ x *(1 + log(x))
x *(1 + log(x))*log\1 + x / + -----------------
x 2*x / x\
1 + x x *(1 + log(x))*log\1 + x /
----------------------------------------------- - -----------------------------
x 2
1 + x / x\
\1 + x /
$$- \frac{x^{2 x} \left(\log{\left(x \right)} + 1\right) \log{\left(x^{x} + 1 \right)}}{\left(x^{x} + 1\right)^{2}} + \frac{\frac{x^{2 x} \left(\log{\left(x \right)} + 1\right)}{x^{x} + 1} + x^{x} \left(\log{\left(x \right)} + 1\right) \log{\left(x^{x} + 1 \right)}}{x^{x} + 1}$$
Segunda derivada
[src]
/ / x 2\ / x 2\ / x \\
| x |1 2 x *(1 + log(x)) | x |1 2 2*x *(1 + log(x)) | / x\ x 2 | x / x\||
| x *|- + (1 + log(x)) - ----------------| x *|- + (1 + log(x)) - ------------------|*log\1 + x / 2*x *(1 + log(x)) *|------ + log\1 + x /||
| |x x | x 2 |x x | | x ||
x |/1 2\ / x\ \ 1 + x / 2*x *(1 + log(x)) \ 1 + x / \1 + x /|
x *||- + (1 + log(x)) |*log\1 + x / + ----------------------------------------- + ------------------ - ------------------------------------------------------- - -----------------------------------------|
|\x / x x x x |
\ 1 + x 1 + x 1 + x 1 + x /
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
x
1 + x
$$\frac{x^{x} \left(- \frac{2 x^{x} \left(\frac{x^{x}}{x^{x} + 1} + \log{\left(x^{x} + 1 \right)}\right) \left(\log{\left(x \right)} + 1\right)^{2}}{x^{x} + 1} + \frac{2 x^{x} \left(\log{\left(x \right)} + 1\right)^{2}}{x^{x} + 1} - \frac{x^{x} \left(- \frac{2 x^{x} \left(\log{\left(x \right)} + 1\right)^{2}}{x^{x} + 1} + \left(\log{\left(x \right)} + 1\right)^{2} + \frac{1}{x}\right) \log{\left(x^{x} + 1 \right)}}{x^{x} + 1} + \frac{x^{x} \left(- \frac{x^{x} \left(\log{\left(x \right)} + 1\right)^{2}}{x^{x} + 1} + \left(\log{\left(x \right)} + 1\right)^{2} + \frac{1}{x}\right)}{x^{x} + 1} + \left(\left(\log{\left(x \right)} + 1\right)^{2} + \frac{1}{x}\right) \log{\left(x^{x} + 1 \right)}\right)}{x^{x} + 1}$$
Tercera derivada
[src]
/ / / x 2\ \ \
| | x |1 2 x *(1 + log(x)) | | |
| / x 3 2*x 3 x \ / x 3 2*x 3 x \ | x *|- + (1 + log(x)) - ----------------| | |
| x | 3 1 3*(1 + log(x)) 3*x *(1 + log(x)) 2*x *(1 + log(x)) 3*x *(1 + log(x))| x | 3 1 3*(1 + log(x)) 6*x *(1 + log(x)) 6*x *(1 + log(x)) 6*x *(1 + log(x))| / x\ | |x x | x 2| / x 2\ / x \ / x 2\|
| x *|(1 + log(x)) - -- + -------------- - ------------------ + -------------------- - -----------------| x *|(1 + log(x)) - -- + -------------- - ------------------ + -------------------- - -----------------|*log\1 + x / x |/1 2\ / x\ \ 1 + x / 2*x *(1 + log(x)) | x |1 2 x *(1 + log(x)) | x | x / x\| |1 2 2*x *(1 + log(x)) ||
| | 2 x x 2 / x\ | | 2 x x 2 / x\ | 3*x *(1 + log(x))*||- + (1 + log(x)) |*log\1 + x / + ----------------------------------------- + ------------------| x /1 2\ 3*x *(1 + log(x))*|- + (1 + log(x)) - ----------------| 3*x *(1 + log(x))*|------ + log\1 + x /|*|- + (1 + log(x)) - ------------------||
| | x 1 + x / x\ x*\1 + x / | | x 1 + x / x\ x*\1 + x / | |\x / x x | 3*x *(1 + log(x))*|- + (1 + log(x)) | |x x | | x | |x x ||
x |/ 3 1 3*(1 + log(x))\ / x\ \ \1 + x / / \ \1 + x / / \ 1 + x 1 + x / \x / \ 1 + x / \1 + x / \ 1 + x /|
x *||(1 + log(x)) - -- + --------------|*log\1 + x / + -------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------- + ------------------------------------- + -------------------------------------------------------- - ---------------------------------------------------------------------------------|
|| 2 x | x x x x x x |
\\ x / 1 + x 1 + x 1 + x 1 + x 1 + x 1 + x /
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
x
1 + x
$$\frac{x^{x} \left(- \frac{3 x^{x} \left(\frac{x^{x}}{x^{x} + 1} + \log{\left(x^{x} + 1 \right)}\right) \left(\log{\left(x \right)} + 1\right) \left(- \frac{2 x^{x} \left(\log{\left(x \right)} + 1\right)^{2}}{x^{x} + 1} + \left(\log{\left(x \right)} + 1\right)^{2} + \frac{1}{x}\right)}{x^{x} + 1} + \frac{3 x^{x} \left(\left(\log{\left(x \right)} + 1\right)^{2} + \frac{1}{x}\right) \left(\log{\left(x \right)} + 1\right)}{x^{x} + 1} + \frac{3 x^{x} \left(\log{\left(x \right)} + 1\right) \left(- \frac{x^{x} \left(\log{\left(x \right)} + 1\right)^{2}}{x^{x} + 1} + \left(\log{\left(x \right)} + 1\right)^{2} + \frac{1}{x}\right)}{x^{x} + 1} - \frac{3 x^{x} \left(\log{\left(x \right)} + 1\right) \left(\frac{2 x^{x} \left(\log{\left(x \right)} + 1\right)^{2}}{x^{x} + 1} + \frac{x^{x} \left(- \frac{x^{x} \left(\log{\left(x \right)} + 1\right)^{2}}{x^{x} + 1} + \left(\log{\left(x \right)} + 1\right)^{2} + \frac{1}{x}\right)}{x^{x} + 1} + \left(\left(\log{\left(x \right)} + 1\right)^{2} + \frac{1}{x}\right) \log{\left(x^{x} + 1 \right)}\right)}{x^{x} + 1} + \frac{x^{x} \left(\frac{2 x^{2 x} \left(\log{\left(x \right)} + 1\right)^{3}}{\left(x^{x} + 1\right)^{2}} - \frac{3 x^{x} \left(\log{\left(x \right)} + 1\right)^{3}}{x^{x} + 1} + \left(\log{\left(x \right)} + 1\right)^{3} - \frac{3 x^{x} \left(\log{\left(x \right)} + 1\right)}{x \left(x^{x} + 1\right)} + \frac{3 \left(\log{\left(x \right)} + 1\right)}{x} - \frac{1}{x^{2}}\right)}{x^{x} + 1} - \frac{x^{x} \left(\frac{6 x^{2 x} \left(\log{\left(x \right)} + 1\right)^{3}}{\left(x^{x} + 1\right)^{2}} - \frac{6 x^{x} \left(\log{\left(x \right)} + 1\right)^{3}}{x^{x} + 1} + \left(\log{\left(x \right)} + 1\right)^{3} - \frac{6 x^{x} \left(\log{\left(x \right)} + 1\right)}{x \left(x^{x} + 1\right)} + \frac{3 \left(\log{\left(x \right)} + 1\right)}{x} - \frac{1}{x^{2}}\right) \log{\left(x^{x} + 1 \right)}}{x^{x} + 1} + \left(\left(\log{\left(x \right)} + 1\right)^{3} + \frac{3 \left(\log{\left(x \right)} + 1\right)}{x} - \frac{1}{x^{2}}\right) \log{\left(x^{x} + 1 \right)}\right)}{x^{x} + 1}$$
4-я производная
[src]
/ / / x 3 2*x 3 x \ \ \
| / / x 2\ \ | x | 3 1 3*(1 + log(x)) 3*x *(1 + log(x)) 2*x *(1 + log(x)) 3*x *(1 + log(x))| / x 2\| |
| | x |1 2 x *(1 + log(x)) | | | x *|(1 + log(x)) - -- + -------------- - ------------------ + -------------------- - -----------------| x |1 2 x *(1 + log(x)) || |
| / 2 x 4 3*x 4 x 2*x 4 x 2 x 2*x 2\ / 2 3*x 4 x 4 x 2*x 4 x 2 x 2*x 2\ | x *|- + (1 + log(x)) - ----------------| | | | 2 x x 2 / x\ | x /1 2\ 3*x *(1 + log(x))*|- + (1 + log(x)) - ----------------|| / x 3 2*x 3 x \ / x \ / x 3 2*x 3 x \|
| x | 4 2 3 4*(1 + log(x)) 6*(1 + log(x)) 7*x *(1 + log(x)) 6*x *(1 + log(x)) 3*x 12*x *(1 + log(x)) 18*x *(1 + log(x)) 4*x *(1 + log(x)) 12*x *(1 + log(x)) | x | 4 2 3 4*(1 + log(x)) 6*(1 + log(x)) 24*x *(1 + log(x)) 14*x *(1 + log(x)) 6*x 36*x *(1 + log(x)) 36*x *(1 + log(x)) 8*x *(1 + log(x)) 36*x *(1 + log(x)) | / x\ / x 2\ | |x x | x 2| | | x 1 + x / x\ x*\1 + x / | 3*x *(1 + log(x))*|- + (1 + log(x)) | |x x || x | 3 1 3*(1 + log(x)) 3*x *(1 + log(x)) 2*x *(1 + log(x)) 3*x *(1 + log(x))| / x 2\ x | x / x\| | 3 1 3*(1 + log(x)) 6*x *(1 + log(x)) 6*x *(1 + log(x)) 6*x *(1 + log(x))||
| x *|(1 + log(x)) + -- + -- - -------------- + --------------- - ------------------ - -------------------- - ----------- + --------------------- - ------------------- + ----------------- + ---------------------| x *|(1 + log(x)) + -- + -- - -------------- + --------------- - --------------------- - ------------------- - ----------- + --------------------- - ------------------- + ----------------- + ---------------------|*log\1 + x / x |1 2 2*x *(1 + log(x)) | |/1 2\ / x\ \ 1 + x / 2*x *(1 + log(x)) | x |/ 3 1 3*(1 + log(x))\ / x\ \ \1 + x / / \x / \ 1 + x /| x / 3 1 3*(1 + log(x))\ 4*x *(1 + log(x))*|(1 + log(x)) - -- + -------------- - ------------------ + -------------------- - -----------------| x /1 2\ |1 2 x *(1 + log(x)) | 4*x *(1 + log(x))*|------ + log\1 + x /|*|(1 + log(x)) - -- + -------------- - ------------------ + -------------------- - -----------------||
| | 3 2 2 x x 3 2 / x\ 2 / x\ 2 / x\ 2 | | 3 2 2 x 3 x 2 / x\ 2 / x\ 2 / x\ 2 | 6*x *|- + (1 + log(x)) - ------------------|*||- + (1 + log(x)) |*log\1 + x / + ----------------------------------------- + ------------------| 4*x *(1 + log(x))*||(1 + log(x)) - -- + --------------|*log\1 + x / + -------------------------------------------------------------------------------------------------------- + ------------------------------------- + --------------------------------------------------------| 4*x *(1 + log(x))*|(1 + log(x)) - -- + --------------| | 2 x x 2 / x\ | 6*x *|- + (1 + log(x)) |*|- + (1 + log(x)) - ----------------| | x | | 2 x x 2 / x\ ||
|/ 2\ | x x x 1 + x / x\ x *\1 + x / / x\ x*\1 + x / x *\1 + x / / x\ | | x x x / x\ 1 + x x *\1 + x / / x\ x*\1 + x / x *\1 + x / / x\ | |x x | |\x / x x | || 2 x | x x x | | 2 x | | x 1 + x / x\ x*\1 + x / | \x / |x x | \1 + x / | x 1 + x / x\ x*\1 + x / ||
x || 4 2 3 4*(1 + log(x)) 6*(1 + log(x)) | / x\ \ \1 + x / \1 + x / x*\1 + x / / \ \1 + x / \1 + x / x*\1 + x / / \ 1 + x / \ 1 + x 1 + x / \\ x / 1 + x 1 + x 1 + x / \ x / \ \1 + x / / \ 1 + x / \ \1 + x / /|
x *||(1 + log(x)) + -- + -- - -------------- + ---------------|*log\1 + x / + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------ - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------|
|| 3 2 2 x | x x x x x x x x |
\\ x x x / 1 + x 1 + x 1 + x 1 + x 1 + x 1 + x 1 + x 1 + x /
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
x
1 + x
$$\frac{x^{x} \left(- \frac{4 x^{x} \left(\frac{x^{x}}{x^{x} + 1} + \log{\left(x^{x} + 1 \right)}\right) \left(\log{\left(x \right)} + 1\right) \left(\frac{6 x^{2 x} \left(\log{\left(x \right)} + 1\right)^{3}}{\left(x^{x} + 1\right)^{2}} - \frac{6 x^{x} \left(\log{\left(x \right)} + 1\right)^{3}}{x^{x} + 1} + \left(\log{\left(x \right)} + 1\right)^{3} - \frac{6 x^{x} \left(\log{\left(x \right)} + 1\right)}{x \left(x^{x} + 1\right)} + \frac{3 \left(\log{\left(x \right)} + 1\right)}{x} - \frac{1}{x^{2}}\right)}{x^{x} + 1} + \frac{6 x^{x} \left(\left(\log{\left(x \right)} + 1\right)^{2} + \frac{1}{x}\right) \left(- \frac{x^{x} \left(\log{\left(x \right)} + 1\right)^{2}}{x^{x} + 1} + \left(\log{\left(x \right)} + 1\right)^{2} + \frac{1}{x}\right)}{x^{x} + 1} + \frac{4 x^{x} \left(\log{\left(x \right)} + 1\right) \left(\left(\log{\left(x \right)} + 1\right)^{3} + \frac{3 \left(\log{\left(x \right)} + 1\right)}{x} - \frac{1}{x^{2}}\right)}{x^{x} + 1} - \frac{4 x^{x} \left(\log{\left(x \right)} + 1\right) \left(\frac{3 x^{x} \left(\left(\log{\left(x \right)} + 1\right)^{2} + \frac{1}{x}\right) \left(\log{\left(x \right)} + 1\right)}{x^{x} + 1} + \frac{3 x^{x} \left(\log{\left(x \right)} + 1\right) \left(- \frac{x^{x} \left(\log{\left(x \right)} + 1\right)^{2}}{x^{x} + 1} + \left(\log{\left(x \right)} + 1\right)^{2} + \frac{1}{x}\right)}{x^{x} + 1} + \frac{x^{x} \left(\frac{2 x^{2 x} \left(\log{\left(x \right)} + 1\right)^{3}}{\left(x^{x} + 1\right)^{2}} - \frac{3 x^{x} \left(\log{\left(x \right)} + 1\right)^{3}}{x^{x} + 1} + \left(\log{\left(x \right)} + 1\right)^{3} - \frac{3 x^{x} \left(\log{\left(x \right)} + 1\right)}{x \left(x^{x} + 1\right)} + \frac{3 \left(\log{\left(x \right)} + 1\right)}{x} - \frac{1}{x^{2}}\right)}{x^{x} + 1} + \left(\left(\log{\left(x \right)} + 1\right)^{3} + \frac{3 \left(\log{\left(x \right)} + 1\right)}{x} - \frac{1}{x^{2}}\right) \log{\left(x^{x} + 1 \right)}\right)}{x^{x} + 1} + \frac{4 x^{x} \left(\log{\left(x \right)} + 1\right) \left(\frac{2 x^{2 x} \left(\log{\left(x \right)} + 1\right)^{3}}{\left(x^{x} + 1\right)^{2}} - \frac{3 x^{x} \left(\log{\left(x \right)} + 1\right)^{3}}{x^{x} + 1} + \left(\log{\left(x \right)} + 1\right)^{3} - \frac{3 x^{x} \left(\log{\left(x \right)} + 1\right)}{x \left(x^{x} + 1\right)} + \frac{3 \left(\log{\left(x \right)} + 1\right)}{x} - \frac{1}{x^{2}}\right)}{x^{x} + 1} - \frac{6 x^{x} \left(- \frac{2 x^{x} \left(\log{\left(x \right)} + 1\right)^{2}}{x^{x} + 1} + \left(\log{\left(x \right)} + 1\right)^{2} + \frac{1}{x}\right) \left(\frac{2 x^{x} \left(\log{\left(x \right)} + 1\right)^{2}}{x^{x} + 1} + \frac{x^{x} \left(- \frac{x^{x} \left(\log{\left(x \right)} + 1\right)^{2}}{x^{x} + 1} + \left(\log{\left(x \right)} + 1\right)^{2} + \frac{1}{x}\right)}{x^{x} + 1} + \left(\left(\log{\left(x \right)} + 1\right)^{2} + \frac{1}{x}\right) \log{\left(x^{x} + 1 \right)}\right)}{x^{x} + 1} - \frac{x^{x} \left(- \frac{24 x^{3 x} \left(\log{\left(x \right)} + 1\right)^{4}}{\left(x^{x} + 1\right)^{3}} + \frac{36 x^{2 x} \left(\log{\left(x \right)} + 1\right)^{4}}{\left(x^{x} + 1\right)^{2}} - \frac{14 x^{x} \left(\log{\left(x \right)} + 1\right)^{4}}{x^{x} + 1} + \left(\log{\left(x \right)} + 1\right)^{4} + \frac{36 x^{2 x} \left(\log{\left(x \right)} + 1\right)^{2}}{x \left(x^{x} + 1\right)^{2}} - \frac{36 x^{x} \left(\log{\left(x \right)} + 1\right)^{2}}{x \left(x^{x} + 1\right)} + \frac{6 \left(\log{\left(x \right)} + 1\right)^{2}}{x} + \frac{8 x^{x} \left(\log{\left(x \right)} + 1\right)}{x^{2} \left(x^{x} + 1\right)} - \frac{6 x^{x}}{x^{2} \left(x^{x} + 1\right)} - \frac{4 \left(\log{\left(x \right)} + 1\right)}{x^{2}} + \frac{3}{x^{2}} + \frac{2}{x^{3}}\right) \log{\left(x^{x} + 1 \right)}}{x^{x} + 1} + \frac{x^{x} \left(- \frac{6 x^{3 x} \left(\log{\left(x \right)} + 1\right)^{4}}{\left(x^{x} + 1\right)^{3}} + \frac{12 x^{2 x} \left(\log{\left(x \right)} + 1\right)^{4}}{\left(x^{x} + 1\right)^{2}} - \frac{7 x^{x} \left(\log{\left(x \right)} + 1\right)^{4}}{x^{x} + 1} + \left(\log{\left(x \right)} + 1\right)^{4} + \frac{12 x^{2 x} \left(\log{\left(x \right)} + 1\right)^{2}}{x \left(x^{x} + 1\right)^{2}} - \frac{18 x^{x} \left(\log{\left(x \right)} + 1\right)^{2}}{x \left(x^{x} + 1\right)} + \frac{6 \left(\log{\left(x \right)} + 1\right)^{2}}{x} + \frac{4 x^{x} \left(\log{\left(x \right)} + 1\right)}{x^{2} \left(x^{x} + 1\right)} - \frac{3 x^{x}}{x^{2} \left(x^{x} + 1\right)} - \frac{4 \left(\log{\left(x \right)} + 1\right)}{x^{2}} + \frac{3}{x^{2}} + \frac{2}{x^{3}}\right)}{x^{x} + 1} + \left(\left(\log{\left(x \right)} + 1\right)^{4} + \frac{6 \left(\log{\left(x \right)} + 1\right)^{2}}{x} - \frac{4 \left(\log{\left(x \right)} + 1\right)}{x^{2}} + \frac{3}{x^{2}} + \frac{2}{x^{3}}\right) \log{\left(x^{x} + 1 \right)}\right)}{x^{x} + 1}$$
Gráfico