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Derivada de:
Derivada de x^-7
Derivada de i*n*x
Derivada de (x+7)^5
Derivada de 1/x^9
Expresiones idénticas
z=e^((t^ dos /ln(t))^ uno / dos)
z es igual a e en el grado ((t al cuadrado dividir por ln(t)) en el grado 1 dividir por 2)
z es igual a e en el grado ((t en el grado dos dividir por ln(t)) en el grado uno dividir por dos)
z=e((t2/ln(t))1/2)
z=et2/lnt1/2
z=e^((t²/ln(t))^1/2)
z=e en el grado ((t en el grado 2/ln(t)) en el grado 1/2)
z=e^t^2/lnt^1/2
z=e^((t^2 dividir por ln(t))^1 dividir por 2)
Expresiones con funciones
ln
ln(e^(2*x)+1)
ln(3x²)
ln(x+8)
ln(x^(1÷2)+2)
ln((x^2+4)/x)

Derivada de la función/ ln(t)/ z=e^((t^2/ln(t))^1/2)

Derivada de z=e^((t^2/ln(t))^1/2)

Solución

Ha introducido [src]

      ________
     /    2   
    /    t    
   /   ------ 
 \/    log(t) 
E

e^{\sqrt{\frac{t^{2}}{\log{\left(t \right)}}}}

E^(sqrt(t^2/log(t)))

Solución detallada

Sustituimos $u = \sqrt{\frac{t^{2}}{\log{\left(t \right)}}}$ .
Derivado $e^{u}$ es.
Luego se aplica una cadena de reglas. Multiplicamos por $\frac{d}{d t} \sqrt{\frac{t^{2}}{\log{\left(t \right)}}}$ :
1. Sustituimos $u = \frac{t^{2}}{\log{\left(t \right)}}$ .
2. Según el principio, aplicamos: $\sqrt{u}$ tenemos $\frac{1}{2 \sqrt{u}}$
3. Luego se aplica una cadena de reglas. Multiplicamos por $\frac{d}{d t} \frac{t^{2}}{\log{\left(t \right)}}$ :
  1. Se aplica la regla de la derivada parcial:
    
    $\frac{d}{d t} \frac{f{\left(t \right)}}{g{\left(t \right)}} = \frac{- f{\left(t \right)} \frac{d}{d t} g{\left(t \right)} + g{\left(t \right)} \frac{d}{d t} f{\left(t \right)}}{g^{2}{\left(t \right)}}$
    
    $f{\left(t \right)} = t^{2}$ y $g{\left(t \right)} = \log{\left(t \right)}$ .
    
    Para calcular $\frac{d}{d t} f{\left(t \right)}$ :
    1. Según el principio, aplicamos: $t^{2}$ tenemos $2 t$
    Para calcular $\frac{d}{d t} g{\left(t \right)}$ :
    1. Derivado $\log{\left(t \right)}$ es $\frac{1}{t}$ .
    Ahora aplicamos la regla de la derivada de una divesión:
    
    $\frac{2 t \log{\left(t \right)} - t}{\log{\left(t \right)}^{2}}$
  Como resultado de la secuencia de reglas:
  
  $\frac{2 t \log{\left(t \right)} - t}{2 \sqrt{\frac{1}{\log{\left(t \right)}}} \log{\left(t \right)}^{2} \left|{t}\right|}$
Como resultado de la secuencia de reglas:

$\frac{\left(2 t \log{\left(t \right)} - t\right) e^{\sqrt{\frac{t^{2}}{\log{\left(t \right)}}}}}{2 \sqrt{\frac{1}{\log{\left(t \right)}}} \log{\left(t \right)}^{2} \left|{t}\right|}$
Simplificamos:

$\frac{t \left(2 \log{\left(t \right)} - 1\right) e^{\sqrt{\frac{1}{\log{\left(t \right)}}} \left|{t}\right|}}{2 \sqrt{\frac{1}{\log{\left(t \right)}}} \log{\left(t \right)}^{2} \left|{t}\right|}$

Respuesta:

$\frac{t \left(2 \log{\left(t \right)} - 1\right) e^{\sqrt{\frac{1}{\log{\left(t \right)}}} \left|{t}\right|}}{2 \sqrt{\frac{1}{\log{\left(t \right)}}} \log{\left(t \right)}^{2} \left|{t}\right|}$

Primera derivada [src]

                                            ________       
                                           /    2          
                                          /    t           
    ________                             /   ------        
   /   1     /  t          t    \      \/    log(t)        
  /  ------ *|------ - ---------|*|t|*e             *log(t)
\/   log(t)  |log(t)        2   |                          
             \         2*log (t)/                          
-----------------------------------------------------------
                              2                            
                             t

\frac{\left(\frac{t}{\log{\left(t \right)}} - \frac{t}{2 \log{\left(t \right)}^{2}}\right) \sqrt{\frac{1}{\log{\left(t \right)}}} e^{\sqrt{\frac{t^{2}}{\log{\left(t \right)}}}} \log{\left(t \right)} \left|{t}\right|}{t^{2}}

Simplificar

Segunda derivada [src]

/                                                        ________                                                                                           \       ________
|            2       ________                           /   1     /      3         2   \           ________                        ________                 |      /    2   
|/      1   \       /   1     /      1   \             /  ------ *|2 - ------ + -------|*|t|      /   1     /      1   \          /   1     /      1   \    |     /    t    
||2 - ------|      /  ------ *|2 - ------|*sign(t)   \/   log(t)  |    log(t)      2   |         /  ------ *|2 - ------|*|t|     /  ------ *|2 - ------|*|t||    /   ------ 
|\    log(t)/    \/   log(t)  \    log(t)/                        \             log (t)/       \/   log(t)  \    log(t)/       \/   log(t)  \    log(t)/    |  \/    log(t) 
|------------- + --------------------------------- + --------------------------------------- - ----------------------------- + -----------------------------|*e             
|   4*log(t)                    2*t                                       2                                   2                            2                |               
\                                                                      2*t                                   t                          4*t *log(t)         /

\left(\frac{\left(2 - \frac{1}{\log{\left(t \right)}}\right)^{2}}{4 \log{\left(t \right)}} + \frac{\left(2 - \frac{1}{\log{\left(t \right)}}\right) \sqrt{\frac{1}{\log{\left(t \right)}}} \operatorname{sign}{\left(t \right)}}{2 t} - \frac{\left(2 - \frac{1}{\log{\left(t \right)}}\right) \sqrt{\frac{1}{\log{\left(t \right)}}} \left|{t}\right|}{t^{2}} + \frac{\left(2 - \frac{1}{\log{\left(t \right)}}\right) \sqrt{\frac{1}{\log{\left(t \right)}}} \left|{t}\right|}{4 t^{2} \log{\left(t \right)}} + \frac{\left(2 - \frac{3}{\log{\left(t \right)}} + \frac{2}{\log{\left(t \right)}^{2}}\right) \sqrt{\frac{1}{\log{\left(t \right)}}} \left|{t}\right|}{2 t^{2}}\right) e^{\sqrt{\frac{t^{2}}{\log{\left(t \right)}}}}

Simplificar

Tercera derivada [src]

/                                                                                                                          ________                                                                              ________                                                                                                                                         ________                                  ________                                                                                                                         \       ________
|              2                 2                                               /      1   \ /      3         2   \      /   1     /      3         2   \                 ________                             /   1     /      3         2   \             ________                        ________             3           ________                           /   1     /      3         2   \          /   1     /      3         3   \             ________                        ________                                2            |      /    2   
|  /      1   \      /      1   \                                              3*|2 - ------|*|2 - ------ + -------|     /  ------ *|2 - ------ + -------|*sign(t)        /   1     /      1   \           2*  /  ------ *|2 - ------ + -------|*|t|        /   1     /      1   \          /   1     /      1   \           /   1     /      1   \             /  ------ *|2 - ------ + -------|*|t|     /  ------ *|1 - ------ + -------|*|t|        /   1     /      1   \          /   1     /      1   \       /      1   \             |     /    t    
|  |2 - ------|    3*|2 - ------|        ________                                \    log(t)/ |    log(t)      2   |   \/   log(t)  |    log(t)      2   |           2*  /  ------ *|2 - ------|*sign(t)     \/   log(t)  |    log(t)      2   |       3*  /  ------ *|2 - ------|*|t|     /  ------ *|2 - ------| *|t|     /  ------ *|2 - ------|*sign(t)   \/   log(t)  |    log(t)      2   |       \/   log(t)  |    log(t)      2   |       5*  /  ------ *|2 - ------|*|t|     /  ------ *|2 - ------|*|t|   |2 - ------| *|t|*sign(t)|    /   ------ 
|  \    log(t)/      \    log(t)/       /   1     /      1   \                                \             log (t)/                \             log (t)/             \/   log(t)  \    log(t)/                          \             log (t)/         \/   log(t)  \    log(t)/       \/   log(t)  \    log(t)/        \/   log(t)  \    log(t)/                        \             log (t)/                    \             log (t)/         \/   log(t)  \    log(t)/       \/   log(t)  \    log(t)/       \    log(t)/             |  \/    log(t) 
|- ------------- + --------------- +   /  ------ *|2 - ------|*DiracDelta(t) + ------------------------------------- + ------------------------------------------- - ----------------------------------- - ----------------------------------------- + ------------------------------- + ------------------------------ + --------------------------------- + --------------------------------------- - --------------------------------------- - ------------------------------- - ----------------------------- + -------------------------|*e             
|      log(t)              2         \/   log(t)  \    log(t)/                                4*log(t)                                      t                                         t                                         2                                      2                            8*log(t)                          2*t*log(t)                               2                                        2                                      2                                2    2                      4*t*log(t)       |               
\                     8*log (t)                                                                                                                                                                                                t                                      t                                                                                                     2*t *log(t)                                t *log(t)                            4*t *log(t)                      8*t *log (t)                                    /               
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                                                                                                                                              t

\frac{\left(\frac{\left(2 - \frac{1}{\log{\left(t \right)}}\right)^{3} \sqrt{\frac{1}{\log{\left(t \right)}}} \left|{t}\right|}{8 \log{\left(t \right)}} - \frac{\left(2 - \frac{1}{\log{\left(t \right)}}\right)^{2}}{\log{\left(t \right)}} + \frac{3 \left(2 - \frac{1}{\log{\left(t \right)}}\right)^{2}}{8 \log{\left(t \right)}^{2}} + \frac{3 \left(2 - \frac{1}{\log{\left(t \right)}}\right) \left(2 - \frac{3}{\log{\left(t \right)}} + \frac{2}{\log{\left(t \right)}^{2}}\right)}{4 \log{\left(t \right)}} + \left(2 - \frac{1}{\log{\left(t \right)}}\right) \sqrt{\frac{1}{\log{\left(t \right)}}} \delta\left(t\right) + \frac{\left(2 - \frac{1}{\log{\left(t \right)}}\right)^{2} \left|{t}\right| \operatorname{sign}{\left(t \right)}}{4 t \log{\left(t \right)}} - \frac{2 \left(2 - \frac{1}{\log{\left(t \right)}}\right) \sqrt{\frac{1}{\log{\left(t \right)}}} \operatorname{sign}{\left(t \right)}}{t} + \frac{\left(2 - \frac{1}{\log{\left(t \right)}}\right) \sqrt{\frac{1}{\log{\left(t \right)}}} \operatorname{sign}{\left(t \right)}}{2 t \log{\left(t \right)}} + \frac{\left(2 - \frac{3}{\log{\left(t \right)}} + \frac{2}{\log{\left(t \right)}^{2}}\right) \sqrt{\frac{1}{\log{\left(t \right)}}} \operatorname{sign}{\left(t \right)}}{t} + \frac{3 \left(2 - \frac{1}{\log{\left(t \right)}}\right) \sqrt{\frac{1}{\log{\left(t \right)}}} \left|{t}\right|}{t^{2}} - \frac{5 \left(2 - \frac{1}{\log{\left(t \right)}}\right) \sqrt{\frac{1}{\log{\left(t \right)}}} \left|{t}\right|}{4 t^{2} \log{\left(t \right)}} - \frac{\left(2 - \frac{1}{\log{\left(t \right)}}\right) \sqrt{\frac{1}{\log{\left(t \right)}}} \left|{t}\right|}{8 t^{2} \log{\left(t \right)}^{2}} - \frac{\left(1 - \frac{3}{\log{\left(t \right)}} + \frac{3}{\log{\left(t \right)}^{2}}\right) \sqrt{\frac{1}{\log{\left(t \right)}}} \left|{t}\right|}{t^{2} \log{\left(t \right)}} - \frac{2 \left(2 - \frac{3}{\log{\left(t \right)}} + \frac{2}{\log{\left(t \right)}^{2}}\right) \sqrt{\frac{1}{\log{\left(t \right)}}} \left|{t}\right|}{t^{2}} + \frac{\left(2 - \frac{3}{\log{\left(t \right)}} + \frac{2}{\log{\left(t \right)}^{2}}\right) \sqrt{\frac{1}{\log{\left(t \right)}}} \left|{t}\right|}{2 t^{2} \log{\left(t \right)}}\right) e^{\sqrt{\frac{t^{2}}{\log{\left(t \right)}}}}}{t}

Simplificar

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Derivada de z=e^((t^2/ln(t))^1/2)

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Solución