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Derivada de:
Derivada de e^((3*x)^2)
Derivada de d/dx(x)
Derivada de (cos(x))^x^2
Derivada de (8*x-15)^5
Expresiones idénticas
y=(x^ treinta y uno ^x)*(treinta y uno ^x)
y es igual a (x al cubo 1 en el grado x) multiplicar por (31 en el grado x)
y es igual a (x en el grado treinta y uno en el grado x) multiplicar por (treinta y uno en el grado x)
y=(x31x)*(31x)
y=x31x*31x
y=(x³1^x)*(31^x)
y=(x en el grado 31 en el grado x)*(31 en el grado x)
y=(x^31^x)(31^x)
y=(x31x)(31x)
y=x31x31x
y=x^31^x31^x

Derivada de la función/ y=(x^31^x)*(31^x)

Derivada de y=(x^31^x)*(31^x)

Solución

Ha introducido [src]

 /  x\    
 \31 /   x
x     *31

$$31^{x} x^{31^{x}}$$

x^(31^x)*31^x

Solución detallada

Se aplica la regla de la derivada de una multiplicación:

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

$f{\left(x \right)} = x^{31^{x}}$ ; calculamos $\frac{d}{d x} f{\left(x \right)}$ :
1. No logro encontrar los pasos en la búsqueda de esta derivada.
  
  Perola derivada
  
  $31^{31^{x} x} \left(\log{\left(31^{x} \right)} + 1\right)$
$g{\left(x \right)} = 31^{x}$ ; calculamos $\frac{d}{d x} g{\left(x \right)}$ :
1. $\frac{d}{d x} 31^{x} = 31^{x} \log{\left(31 \right)}$
Como resultado de: $31^{x} 31^{31^{x} x} \left(\log{\left(31^{x} \right)} + 1\right) + 31^{x} x^{31^{x}} \log{\left(31 \right)}$
Simplificamos:

$31^{x} x^{31^{x}} \log{\left(31 \right)} + 31^{x \left(31^{x} + 1\right)} \left(x \log{\left(31 \right)} + 1\right)$

Respuesta:

$31^{x} x^{31^{x}} \log{\left(31 \right)} + 31^{x \left(31^{x} + 1\right)} \left(x \log{\left(31 \right)} + 1\right)$

Primera derivada [src]

     /  x\ /  x                     \        /  x\        
  x  \31 / |31      x               |     x  \31 /        
31 *x     *|--- + 31 *log(31)*log(x)| + 31 *x     *log(31)
           \ x                      /

$$31^{x} x^{31^{x}} \left(31^{x} \log{\left(31 \right)} \log{\left(x \right)} + \frac{31^{x}}{x}\right) + 31^{x} x^{31^{x}} \log{\left(31 \right)}$$

Simplificar

Segunda derivada [src]

     /  x\ /               /                               2                              \                                     \
  x  \31 / |   2         x |  1      x /1                 \       2              2*log(31)|       x /1                 \        |
31 *x     *|log (31) + 31 *|- -- + 31 *|- + log(31)*log(x)|  + log (31)*log(x) + ---------| + 2*31 *|- + log(31)*log(x)|*log(31)|
           |               |   2       \x                 /                          x    |         \x                 /        |
           \               \  x                                                           /                                     /

$$31^{x} x^{31^{x}} \left(2 \cdot 31^{x} \left(\log{\left(31 \right)} \log{\left(x \right)} + \frac{1}{x}\right) \log{\left(31 \right)} + 31^{x} \left(31^{x} \left(\log{\left(31 \right)} \log{\left(x \right)} + \frac{1}{x}\right)^{2} + \log{\left(31 \right)}^{2} \log{\left(x \right)} + \frac{2 \log{\left(31 \right)}}{x} - \frac{1}{x^{2}}\right) + \log{\left(31 \right)}^{2}\right)$$

Simplificar

Tercera derivada [src]

     /  x\ /               /                               3                                      2                                                                      \                                               /                               2                              \        \
  x  \31 / |   3         x |2      2*x /1                 \       3              3*log(31)   3*log (31)       x /1                 \ /  1       2              2*log(31)\|       x    2     /1                 \       x |  1      x /1                 \       2              2*log(31)|        |
31 *x     *|log (31) + 31 *|-- + 31   *|- + log(31)*log(x)|  + log (31)*log(x) - --------- + ---------- + 3*31 *|- + log(31)*log(x)|*|- -- + log (31)*log(x) + ---------|| + 3*31 *log (31)*|- + log(31)*log(x)| + 3*31 *|- -- + 31 *|- + log(31)*log(x)|  + log (31)*log(x) + ---------|*log(31)|
           |               | 3         \x                 /                           2          x              \x                 / |   2                         x    ||                  \x                 /         |   2       \x                 /                          x    |        |
           \               \x                                                        x                                               \  x                               //                                               \  x                                                           /        /

$$31^{x} x^{31^{x}} \left(3 \cdot 31^{x} \left(\log{\left(31 \right)} \log{\left(x \right)} + \frac{1}{x}\right) \log{\left(31 \right)}^{2} + 3 \cdot 31^{x} \left(31^{x} \left(\log{\left(31 \right)} \log{\left(x \right)} + \frac{1}{x}\right)^{2} + \log{\left(31 \right)}^{2} \log{\left(x \right)} + \frac{2 \log{\left(31 \right)}}{x} - \frac{1}{x^{2}}\right) \log{\left(31 \right)} + 31^{x} \left(31^{2 x} \left(\log{\left(31 \right)} \log{\left(x \right)} + \frac{1}{x}\right)^{3} + 3 \cdot 31^{x} \left(\log{\left(31 \right)} \log{\left(x \right)} + \frac{1}{x}\right) \left(\log{\left(31 \right)}^{2} \log{\left(x \right)} + \frac{2 \log{\left(31 \right)}}{x} - \frac{1}{x^{2}}\right) + \log{\left(31 \right)}^{3} \log{\left(x \right)} + \frac{3 \log{\left(31 \right)}^{2}}{x} - \frac{3 \log{\left(31 \right)}}{x^{2}} + \frac{2}{x^{3}}\right) + \log{\left(31 \right)}^{3}\right)$$

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Expresiones idénticas

Derivada de y=(x^31^x)*(31^x)

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