Sr Examen

Lang:

Otras calculadoras

¿Cómo usar?
Derivada de:
Derivada de π/17
Derivada de (π/2)*cos(π*t/2)
Derivada de π/20
Derivada de µ(t)y
Expresiones idénticas
y= tres ^(dos ^x*(ln^ tres)x)
y es igual a 3 en el grado (2 en el grado x multiplicar por (ln al cubo )x)
y es igual a tres en el grado (dos en el grado x multiplicar por (ln en el grado tres)x)
y=3(2x*(ln3)x)
y=32x*ln3x
y=3^(2^x*(ln³)x)
y=3 en el grado (2 en el grado x*(ln en el grado 3)x)
y=3^(2^x(ln^3)x)
y=3(2x(ln3)x)
y=32xln3x
y=3^2^xln^3x

Derivada de la función/ y=3^(2^x*(ln^3)x)

Derivada de y=3^(2^x*(ln^3)x)

Solución

Ha introducido [src]

  x    3     
 2 *log (x)*x
3

$$3^{x 2^{x} \log{\left(x \right)}^{3}}$$

3^((2^x*log(x)^3)*x)

Solución detallada

Sustituimos $u = x 2^{x} \log{\left(x \right)}^{3}$ .
$\frac{d}{d u} 3^{u} = 3^{u} \log{\left(3 \right)}$
Luego se aplica una cadena de reglas. Multiplicamos por $\frac{d}{d x} x 2^{x} \log{\left(x \right)}^{3}$ :
1. Se aplica la regla de la derivada de una multiplicación:
  
  $\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$
  
  $f{\left(x \right)} = 2^{x} \log{\left(x \right)}^{3}$ ; calculamos $\frac{d}{d x} f{\left(x \right)}$ :
  1. Se aplica la regla de la derivada de una multiplicación:
    
    $\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$
    
    $f{\left(x \right)} = 2^{x}$ ; calculamos $\frac{d}{d x} f{\left(x \right)}$ :
    1. $\frac{d}{d x} 2^{x} = 2^{x} \log{\left(2 \right)}$
    $g{\left(x \right)} = \log{\left(x \right)}^{3}$ ; calculamos $\frac{d}{d x} g{\left(x \right)}$ :
    1. Sustituimos $u = \log{\left(x \right)}$ .
    2. Según el principio, aplicamos: $u^{3}$ tenemos $3 u^{2}$
    3. Luego se aplica una cadena de reglas. Multiplicamos por $\frac{d}{d x} \log{\left(x \right)}$ :
      1. Derivado $\log{\left(x \right)}$ es $\frac{1}{x}$ .
      Como resultado de la secuencia de reglas:
      
      $\frac{3 \log{\left(x \right)}^{2}}{x}$
    Como resultado de: $2^{x} \log{\left(2 \right)} \log{\left(x \right)}^{3} + \frac{3 \cdot 2^{x} \log{\left(x \right)}^{2}}{x}$
  $g{\left(x \right)} = x$ ; calculamos $\frac{d}{d x} g{\left(x \right)}$ :
  1. Según el principio, aplicamos: $x$ tenemos $1$
  Como resultado de: $2^{x} \log{\left(x \right)}^{3} + x \left(2^{x} \log{\left(2 \right)} \log{\left(x \right)}^{3} + \frac{3 \cdot 2^{x} \log{\left(x \right)}^{2}}{x}\right)$
Como resultado de la secuencia de reglas:

$3^{x 2^{x} \log{\left(x \right)}^{3}} \left(2^{x} \log{\left(x \right)}^{3} + x \left(2^{x} \log{\left(2 \right)} \log{\left(x \right)}^{3} + \frac{3 \cdot 2^{x} \log{\left(x \right)}^{2}}{x}\right)\right) \log{\left(3 \right)}$
Simplificamos:

$2^{x} 3^{2^{x} x \log{\left(x \right)}^{3}} \left(x \log{\left(2 \right)} \log{\left(x \right)} + \log{\left(x \right)} + 3\right) \log{\left(3 \right)} \log{\left(x \right)}^{2}$

Respuesta:

$2^{x} 3^{2^{x} x \log{\left(x \right)}^{3}} \left(x \log{\left(2 \right)} \log{\left(x \right)} + \log{\left(x \right)} + 3\right) \log{\left(3 \right)} \log{\left(x \right)}^{2}$

Primera derivada [src]

  x    3      /  /                       x    2   \             \       
 2 *log (x)*x |  | x    3             3*2 *log (x)|    x    3   |       
3            *|x*|2 *log (x)*log(2) + ------------| + 2 *log (x)|*log(3)
              \  \                         x      /             /

$$3^{x 2^{x} \log{\left(x \right)}^{3}} \left(2^{x} \log{\left(x \right)}^{3} + x \left(2^{x} \log{\left(2 \right)} \log{\left(x \right)}^{3} + \frac{3 \cdot 2^{x} \log{\left(x \right)}^{2}}{x}\right)\right) \log{\left(3 \right)}$$

Simplificar

Segunda derivada [src]

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

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

Simplificar

Tercera derivada [src]

       x    3    /  /                                        2           2                  2       2                      \        2                                            2                                                  3                                                                                                                                                             \       
 x  x*2 *log (x) |  |6       3       3      18*log(x)   6*log (x)   9*log (x)*log(2)   9*log (2)*log (x)   18*log(2)*log(x)|   9*log (x)        2       3      18*log(x)   18*log (x)*log(2)    2*x /  /3                \         \     2       6         x    3    /  /3                \         \ /  /6       2       2      3*log(x)   6*log(2)*log(x)\        2             6*log(x)\       |       
2 *3            *|x*|-- + log (2)*log (x) - --------- + --------- - ---------------- + ----------------- + ----------------| - --------- + 3*log (2)*log (x) + --------- + ----------------- + 2   *|x*|- + log(2)*log(x)| + log(x)| *log (3)*log (x) + 3*2 *log (x)*|x*|- + log(2)*log(x)| + log(x)|*|x*|-- + log (2)*log (x) - -------- + ---------------| + 2*log (x)*log(2) + --------|*log(3)|*log(3)
                 |  | 3                          3           3              2                  x                   2       |        2                               2              x                \  \x                /         /                                 \  \x                /         / |  | 2                         2             x       |                         x    |       |       
                 \  \x                          x           x              x                                      x        /       x                               x                                                                                                                                  \  \x                         x                      /                              /       /

$$2^{x} 3^{2^{x} x \log{\left(x \right)}^{3}} \left(2^{2 x} \left(x \left(\log{\left(2 \right)} \log{\left(x \right)} + \frac{3}{x}\right) + \log{\left(x \right)}\right)^{3} \log{\left(3 \right)}^{2} \log{\left(x \right)}^{6} + 3 \cdot 2^{x} \left(x \left(\log{\left(2 \right)} \log{\left(x \right)} + \frac{3}{x}\right) + \log{\left(x \right)}\right) \left(x \left(\log{\left(2 \right)}^{2} \log{\left(x \right)}^{2} + \frac{6 \log{\left(2 \right)} \log{\left(x \right)}}{x} - \frac{3 \log{\left(x \right)}}{x^{2}} + \frac{6}{x^{2}}\right) + 2 \log{\left(2 \right)} \log{\left(x \right)}^{2} + \frac{6 \log{\left(x \right)}}{x}\right) \log{\left(3 \right)} \log{\left(x \right)}^{3} + x \left(\log{\left(2 \right)}^{3} \log{\left(x \right)}^{3} + \frac{9 \log{\left(2 \right)}^{2} \log{\left(x \right)}^{2}}{x} - \frac{9 \log{\left(2 \right)} \log{\left(x \right)}^{2}}{x^{2}} + \frac{18 \log{\left(2 \right)} \log{\left(x \right)}}{x^{2}} + \frac{6 \log{\left(x \right)}^{2}}{x^{3}} - \frac{18 \log{\left(x \right)}}{x^{3}} + \frac{6}{x^{3}}\right) + 3 \log{\left(2 \right)}^{2} \log{\left(x \right)}^{3} + \frac{18 \log{\left(2 \right)} \log{\left(x \right)}^{2}}{x} - \frac{9 \log{\left(x \right)}^{2}}{x^{2}} + \frac{18 \log{\left(x \right)}}{x^{2}}\right) \log{\left(3 \right)}$$

Simplificar

Otras calculadoras

¿Cómo usar?

Expresiones idénticas

Derivada de y=3^(2^x*(ln^3)x)

Gráfico:

Definida a trozos:

Solución