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Derivada de:
Derivada de 1/(x+1)^2
Derivada de x^12
Derivada de (x+3)/(x-2)
Derivada de (x^3-4)
Expresiones idénticas
y=x^(dos ^(x))* cinco ^(x)
y es igual a x en el grado (2 en el grado (x)) multiplicar por 5 en el grado (x)
y es igual a x en el grado (dos en el grado (x)) multiplicar por cinco en el grado (x)
y=x(2(x))*5(x)
y=x2x*5x
y=x^(2^(x))5^(x)
y=x(2(x))5(x)
y=x2x5x
y=x^2^x5^x

Derivada de la función/ 2^(x)/ 5^(x)/ y=x^(2^(x))*5^(x)

Derivada de y=x^(2^(x))*5^(x)

Solución

Ha introducido [src]

 / x\   
 \2 /  x
x    *5

$$5^{x} x^{2^{x}}$$

x^(2^x)*5^x

Solución detallada

Se aplica la regla de la derivada de una multiplicación:

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

$f{\left(x \right)} = x^{2^{x}}$ ; calculamos $\frac{d}{d x} f{\left(x \right)}$ :
1. No logro encontrar los pasos en la búsqueda de esta derivada.
  
  Perola derivada
  
  $2^{2^{x} x} \left(\log{\left(2^{x} \right)} + 1\right)$
$g{\left(x \right)} = 5^{x}$ ; calculamos $\frac{d}{d x} g{\left(x \right)}$ :
1. $\frac{d}{d x} 5^{x} = 5^{x} \log{\left(5 \right)}$
Como resultado de: $2^{2^{x} x} 5^{x} \left(\log{\left(2^{x} \right)} + 1\right) + 5^{x} x^{2^{x}} \log{\left(5 \right)}$
Simplificamos:

$5^{x} \left(2^{2^{x} x} \left(x \log{\left(2 \right)} + 1\right) + x^{2^{x}} \log{\left(5 \right)}\right)$

Respuesta:

$5^{x} \left(2^{2^{x} x} \left(x \log{\left(2 \right)} + 1\right) + x^{2^{x}} \log{\left(5 \right)}\right)$

Primera derivada [src]

    / x\ / x                   \       / x\       
 x  \2 / |2     x              |    x  \2 /       
5 *x    *|-- + 2 *log(2)*log(x)| + 5 *x    *log(5)
         \x                    /

$$5^{x} x^{2^{x}} \left(2^{x} \log{\left(2 \right)} \log{\left(x \right)} + \frac{2^{x}}{x}\right) + 5^{x} x^{2^{x}} \log{\left(5 \right)}$$

Simplificar

Segunda derivada [src]

 / x\ /                 /                             2                            \                                   \
 \2 / | x    2        x |  1     x /1                \       2             2*log(2)|       x /1                \       |
x    *|5 *log (5) + 10 *|- -- + 2 *|- + log(2)*log(x)|  + log (2)*log(x) + --------| + 2*10 *|- + log(2)*log(x)|*log(5)|
      |                 |   2      \x                /                        x    |         \x                /       |
      \                 \  x                                                       /                                   /

$$x^{2^{x}} \left(2 \cdot 10^{x} \left(\log{\left(2 \right)} \log{\left(x \right)} + \frac{1}{x}\right) \log{\left(5 \right)} + 10^{x} \left(2^{x} \left(\log{\left(2 \right)} \log{\left(x \right)} + \frac{1}{x}\right)^{2} + \log{\left(2 \right)}^{2} \log{\left(x \right)} + \frac{2 \log{\left(2 \right)}}{x} - \frac{1}{x^{2}}\right) + 5^{x} \log{\left(5 \right)}^{2}\right)$$

Simplificar

Tercera derivada [src]

 / x\ /                 /                             3                                    2                                                                 \                                             /                             2                            \       \
 \2 / | x    3        x |2     2*x /1                \       3             3*log(2)   3*log (2)      x /1                \ /  1       2             2*log(2)\|       x    2    /1                \       x |  1     x /1                \       2             2*log(2)|       |
x    *|5 *log (5) + 10 *|-- + 2   *|- + log(2)*log(x)|  + log (2)*log(x) - -------- + --------- + 3*2 *|- + log(2)*log(x)|*|- -- + log (2)*log(x) + --------|| + 3*10 *log (5)*|- + log(2)*log(x)| + 3*10 *|- -- + 2 *|- + log(2)*log(x)|  + log (2)*log(x) + --------|*log(5)|
      |                 | 3        \x                /                         2          x            \x                / |   2                       x    ||                 \x                /         |   2      \x                /                        x    |       |
      \                 \x                                                    x                                            \  x                             //                                             \  x                                                       /       /

$$x^{2^{x}} \left(3 \cdot 10^{x} \left(\log{\left(2 \right)} \log{\left(x \right)} + \frac{1}{x}\right) \log{\left(5 \right)}^{2} + 3 \cdot 10^{x} \left(2^{x} \left(\log{\left(2 \right)} \log{\left(x \right)} + \frac{1}{x}\right)^{2} + \log{\left(2 \right)}^{2} \log{\left(x \right)} + \frac{2 \log{\left(2 \right)}}{x} - \frac{1}{x^{2}}\right) \log{\left(5 \right)} + 10^{x} \left(2^{2 x} \left(\log{\left(2 \right)} \log{\left(x \right)} + \frac{1}{x}\right)^{3} + 3 \cdot 2^{x} \left(\log{\left(2 \right)} \log{\left(x \right)} + \frac{1}{x}\right) \left(\log{\left(2 \right)}^{2} \log{\left(x \right)} + \frac{2 \log{\left(2 \right)}}{x} - \frac{1}{x^{2}}\right) + \log{\left(2 \right)}^{3} \log{\left(x \right)} + \frac{3 \log{\left(2 \right)}^{2}}{x} - \frac{3 \log{\left(2 \right)}}{x^{2}} + \frac{2}{x^{3}}\right) + 5^{x} \log{\left(5 \right)}^{3}\right)$$

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Expresiones idénticas

Derivada de y=x^(2^(x))*5^(x)

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