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Derivada de:
Derivada de (-4)/x^2
Derivada de 2/x²
Derivada de -2*y
Derivada de (3+2x)/(x-5)
Expresiones idénticas
x*exp(siete ^(x)log2(x))
x multiplicar por exponente de (7 en el grado (x) logaritmo de 2(x))
x multiplicar por exponente de (siete en el grado (x) logaritmo de 2(x))
x*exp(7(x)log2(x))
x*exp7xlog2x
xexp(7^(x)log2(x))
xexp(7(x)log2(x))
xexp7xlog2x
xexp7^xlog2x

Derivada de la función/ x*exp/ log2(x)/ x*exp(7^(x)log2(x))

Derivada de x*exp(7^(x)log2(x))

Solución

Ha introducido [src]

    x log(x)
   7 *------
      log(2)
x*e

$$x e^{7^{x} \frac{\log{\left(x \right)}}{\log{\left(2 \right)}}}$$

x*exp(7^x*(log(x)/log(2)))

Solución detallada

Se aplica la regla de la derivada de una multiplicación:

$\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$

$f{\left(x \right)} = x$ ; calculamos $\frac{d}{d x} f{\left(x \right)}$ :
1. Según el principio, aplicamos: $x$ tenemos $1$
$g{\left(x \right)} = e^{7^{x} \frac{\log{\left(x \right)}}{\log{\left(2 \right)}}}$ ; calculamos $\frac{d}{d x} g{\left(x \right)}$ :
1. Sustituimos $u = 7^{x} \frac{\log{\left(x \right)}}{\log{\left(2 \right)}}$ .
2. Derivado $e^{u}$ es.
3. Luego se aplica una cadena de reglas. Multiplicamos por $\frac{d}{d x} 7^{x} \frac{\log{\left(x \right)}}{\log{\left(2 \right)}}$ :
  1. Se aplica la regla de la derivada parcial:
    
    $\frac{d}{d x} \frac{f{\left(x \right)}}{g{\left(x \right)}} = \frac{- f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}}{g^{2}{\left(x \right)}}$
    
    $f{\left(x \right)} = 7^{x} \log{\left(x \right)}$ y $g{\left(x \right)} = \log{\left(2 \right)}$ .
    
    Para calcular $\frac{d}{d x} f{\left(x \right)}$ :
    1. Se aplica la regla de la derivada de una multiplicación:
      
      $\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$
      
      $f{\left(x \right)} = 7^{x}$ ; calculamos $\frac{d}{d x} f{\left(x \right)}$ :
      1. $\frac{d}{d x} 7^{x} = 7^{x} \log{\left(7 \right)}$
      $g{\left(x \right)} = \log{\left(x \right)}$ ; calculamos $\frac{d}{d x} g{\left(x \right)}$ :
      1. Derivado $\log{\left(x \right)}$ es $\frac{1}{x}$ .
      Como resultado de: $7^{x} \log{\left(7 \right)} \log{\left(x \right)} + \frac{7^{x}}{x}$
    Para calcular $\frac{d}{d x} g{\left(x \right)}$ :
    1. La derivada de una constante $\log{\left(2 \right)}$ es igual a cero.
    Ahora aplicamos la regla de la derivada de una divesión:
    
    $\frac{7^{x} \log{\left(7 \right)} \log{\left(x \right)} + \frac{7^{x}}{x}}{\log{\left(2 \right)}}$
  Como resultado de la secuencia de reglas:
  
  $\frac{\left(7^{x} \log{\left(7 \right)} \log{\left(x \right)} + \frac{7^{x}}{x}\right) e^{7^{x} \frac{\log{\left(x \right)}}{\log{\left(2 \right)}}}}{\log{\left(2 \right)}}$
Como resultado de: $\frac{x \left(7^{x} \log{\left(7 \right)} \log{\left(x \right)} + \frac{7^{x}}{x}\right) e^{7^{x} \frac{\log{\left(x \right)}}{\log{\left(2 \right)}}}}{\log{\left(2 \right)}} + e^{7^{x} \frac{\log{\left(x \right)}}{\log{\left(2 \right)}}}$
Simplificamos:

$\frac{\left(7^{x} \left(x \log{\left(7 \right)} \log{\left(x \right)} + 1\right) + \log{\left(2 \right)}\right) e^{\frac{7^{x} \log{\left(x \right)}}{\log{\left(2 \right)}}}}{\log{\left(2 \right)}}$

Respuesta:

$\frac{\left(7^{x} \left(x \log{\left(7 \right)} \log{\left(x \right)} + 1\right) + \log{\left(2 \right)}\right) e^{\frac{7^{x} \log{\left(x \right)}}{\log{\left(2 \right)}}}}{\log{\left(2 \right)}}$

Primera derivada [src]

                                  x log(x)     x log(x)
  /    x       x              \  7 *------    7 *------
  |   7       7 *log(7)*log(x)|     log(2)       log(2)
x*|-------- + ----------------|*e          + e         
  \x*log(2)        log(2)     /

$$x \left(\frac{7^{x} \log{\left(7 \right)} \log{\left(x \right)}}{\log{\left(2 \right)}} + \frac{7^{x}}{x \log{\left(2 \right)}}\right) e^{7^{x} \frac{\log{\left(x \right)}}{\log{\left(2 \right)}}} + e^{7^{x} \frac{\log{\left(x \right)}}{\log{\left(2 \right)}}}$$

Simplificar

Segunda derivada [src]

   /      /                                                         2\                  \   x       
   |      |                                    x /1                \ |                  |  7 *log(x)
   |      |                                   7 *|- + log(7)*log(x)| |                  |  ---------
 x |2     |  1       2             2*log(7)      \x                / |                  |    log(2) 
7 *|- + x*|- -- + log (7)*log(x) + -------- + -----------------------| + 2*log(7)*log(x)|*e         
   |x     |   2                       x                log(2)        |                  |           
   \      \  x                                                       /                  /           
----------------------------------------------------------------------------------------------------
                                               log(2)

$$\frac{7^{x} \left(x \left(\frac{7^{x} \left(\log{\left(7 \right)} \log{\left(x \right)} + \frac{1}{x}\right)^{2}}{\log{\left(2 \right)}} + \log{\left(7 \right)}^{2} \log{\left(x \right)} + \frac{2 \log{\left(7 \right)}}{x} - \frac{1}{x^{2}}\right) + 2 \log{\left(7 \right)} \log{\left(x \right)} + \frac{2}{x}\right) e^{\frac{7^{x} \log{\left(x \right)}}{\log{\left(2 \right)}}}}{\log{\left(2 \right)}}$$

Simplificar

Tercera derivada [src]

   /         /                                                                     3      x /1                \ /  1       2             2*log(7)\\                                                         2\   x       
   |         |                                              2*x /1                \    3*7 *|- + log(7)*log(x)|*|- -- + log (7)*log(x) + --------||                                    x /1                \ |  7 *log(x)
   |         |                                      2      7   *|- + log(7)*log(x)|         \x                / |   2                       x    ||                                 3*7 *|- + log(7)*log(x)| |  ---------
 x |  3      |2       3             3*log(7)   3*log (7)        \x                /                             \  x                             /|        2             6*log(7)        \x                / |    log(2) 
7 *|- -- + x*|-- + log (7)*log(x) - -------- + --------- + ------------------------- + -----------------------------------------------------------| + 3*log (7)*log(x) + -------- + -------------------------|*e         
   |   2     | 3                        2          x                   2                                          log(2)                          |                         x                 log(2)         |           
   \  x      \x                        x                            log (2)                                                                       /                                                          /           
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                          log(2)

$$\frac{7^{x} \left(\frac{3 \cdot 7^{x} \left(\log{\left(7 \right)} \log{\left(x \right)} + \frac{1}{x}\right)^{2}}{\log{\left(2 \right)}} + x \left(\frac{7^{2 x} \left(\log{\left(7 \right)} \log{\left(x \right)} + \frac{1}{x}\right)^{3}}{\log{\left(2 \right)}^{2}} + \frac{3 \cdot 7^{x} \left(\log{\left(7 \right)} \log{\left(x \right)} + \frac{1}{x}\right) \left(\log{\left(7 \right)}^{2} \log{\left(x \right)} + \frac{2 \log{\left(7 \right)}}{x} - \frac{1}{x^{2}}\right)}{\log{\left(2 \right)}} + \log{\left(7 \right)}^{3} \log{\left(x \right)} + \frac{3 \log{\left(7 \right)}^{2}}{x} - \frac{3 \log{\left(7 \right)}}{x^{2}} + \frac{2}{x^{3}}\right) + 3 \log{\left(7 \right)}^{2} \log{\left(x \right)} + \frac{6 \log{\left(7 \right)}}{x} - \frac{3}{x^{2}}\right) e^{\frac{7^{x} \log{\left(x \right)}}{\log{\left(2 \right)}}}}{\log{\left(2 \right)}}$$

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Expresiones idénticas

Derivada de x*exp(7^(x)log2(x))

Gráfico:

Definida a trozos:

Solución