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Derivada de:
Derivada de y=(x ^2-3x+2)(x^2+1)
Derivada de y=x*ln(x+(x^2+a^2)^(1/2))
Derivada de y=x^ln*x
Derivada de y=x×ln×x
Expresiones idénticas
y=(x^ tres ^x)* dos ^x
y es igual a (x al cubo en el grado x) multiplicar por 2 en el grado x
y es igual a (x en el grado tres en el grado x) multiplicar por dos en el grado x
y=(x3x)*2x
y=x3x*2x
y=(x³^x)*2^x
y=(x en el grado 3 en el grado x)*2 en el grado x
y=(x^3^x)2^x
y=(x3x)2x
y=x3x2x
y=x^3^x2^x

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

Solución

Ha introducido [src]

 / x\   
 \3 /  x
x    *2

$$2^{x} x^{3^{x}}$$

x^(3^x)*2^x

Solución detallada

Se aplica la regla de la derivada de una multiplicación:

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

$f{\left(x \right)} = x^{3^{x}}$ ; calculamos $\frac{d}{d x} f{\left(x \right)}$ :
1. No logro encontrar los pasos en la búsqueda de esta derivada.
  
  Perola derivada
  
  $3^{3^{x} x} \left(\log{\left(3^{x} \right)} + 1\right)$
$g{\left(x \right)} = 2^{x}$ ; calculamos $\frac{d}{d x} g{\left(x \right)}$ :
1. $\frac{d}{d x} 2^{x} = 2^{x} \log{\left(2 \right)}$
Como resultado de: $2^{x} 3^{3^{x} x} \left(\log{\left(3^{x} \right)} + 1\right) + 2^{x} x^{3^{x}} \log{\left(2 \right)}$
Simplificamos:

$2^{x} \left(3^{3^{x} x} \left(x \log{\left(3 \right)} + 1\right) + x^{3^{x}} \log{\left(2 \right)}\right)$

Respuesta:

$2^{x} \left(3^{3^{x} x} \left(x \log{\left(3 \right)} + 1\right) + x^{3^{x}} \log{\left(2 \right)}\right)$

Primera derivada [src]

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

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

Simplificar

Segunda derivada [src]

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

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

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Tercera derivada [src]

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

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

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

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