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Derivada de:
Derivada de 1/(x+3)
Derivada de 4*y
Derivada de (-1)/x-3*x
Derivada de y=csc(3x²+1)
Expresiones idénticas
x^(veintisiete ^x)* veintisiete ^x
x en el grado (27 en el grado x) multiplicar por 27 en el grado x
x en el grado (veintisiete en el grado x) multiplicar por veintisiete en el grado x
x(27x)*27x
x27x*27x
x^(27^x)27^x
x(27x)27x
x27x27x
x^27^x27^x

Derivada de x^(27^x)*27^x

Solución

Ha introducido [src]

 /  x\    
 \27 /   x
x     *27

$$27^{x} x^{27^{x}}$$

x^(27^x)*27^x

Solución detallada

Se aplica la regla de la derivada de una multiplicación:

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

$f{\left(x \right)} = x^{27^{x}}$ ; calculamos $\frac{d}{d x} f{\left(x \right)}$ :
1. No logro encontrar los pasos en la búsqueda de esta derivada.
  
  Perola derivada
  
  $27^{27^{x} x} \left(\log{\left(27^{x} \right)} + 1\right)$
$g{\left(x \right)} = 27^{x}$ ; calculamos $\frac{d}{d x} g{\left(x \right)}$ :
1. $\frac{d}{d x} 27^{x} = 27^{x} \log{\left(27 \right)}$
Como resultado de: $27^{x} 27^{27^{x} x} \left(\log{\left(27^{x} \right)} + 1\right) + 27^{x} x^{27^{x}} \log{\left(27 \right)}$
Simplificamos:

$27^{x \left(27^{x} + 1\right)} \left(\log{\left(27^{x} \right)} + 1\right) + x^{27^{x}} \log{\left(27^{27^{x}} \right)}$

Respuesta:

$27^{x \left(27^{x} + 1\right)} \left(\log{\left(27^{x} \right)} + 1\right) + x^{27^{x}} \log{\left(27^{27^{x}} \right)}$

Primera derivada [src]

     /  x\ /  x                     \        /  x\        
  x  \27 / |27      x               |     x  \27 /        
27 *x     *|--- + 27 *log(27)*log(x)| + 27 *x     *log(27)
           \ x                      /

$$27^{x} x^{27^{x}} \left(27^{x} \log{\left(27 \right)} \log{\left(x \right)} + \frac{27^{x}}{x}\right) + 27^{x} x^{27^{x}} \log{\left(27 \right)}$$

Simplificar

Segunda derivada [src]

     /  x\ /               /                               2                              \                                     \
  x  \27 / |   2         x |  1      x /1                 \       2              2*log(27)|       x /1                 \        |
27 *x     *|log (27) + 27 *|- -- + 27 *|- + log(27)*log(x)|  + log (27)*log(x) + ---------| + 2*27 *|- + log(27)*log(x)|*log(27)|
           |               |   2       \x                 /                          x    |         \x                 /        |
           \               \  x                                                           /                                     /

$$27^{x} x^{27^{x}} \left(2 \cdot 27^{x} \left(\log{\left(27 \right)} \log{\left(x \right)} + \frac{1}{x}\right) \log{\left(27 \right)} + 27^{x} \left(27^{x} \left(\log{\left(27 \right)} \log{\left(x \right)} + \frac{1}{x}\right)^{2} + \log{\left(27 \right)}^{2} \log{\left(x \right)} + \frac{2 \log{\left(27 \right)}}{x} - \frac{1}{x^{2}}\right) + \log{\left(27 \right)}^{2}\right)$$

Simplificar

Tercera derivada [src]

     /  x\ /               /                               3                                      2                                                                      \                                               /                               2                              \        \
  x  \27 / |   3         x |2      2*x /1                 \       3              3*log(27)   3*log (27)       x /1                 \ /  1       2              2*log(27)\|       x    2     /1                 \       x |  1      x /1                 \       2              2*log(27)|        |
27 *x     *|log (27) + 27 *|-- + 27   *|- + log(27)*log(x)|  + log (27)*log(x) - --------- + ---------- + 3*27 *|- + log(27)*log(x)|*|- -- + log (27)*log(x) + ---------|| + 3*27 *log (27)*|- + log(27)*log(x)| + 3*27 *|- -- + 27 *|- + log(27)*log(x)|  + log (27)*log(x) + ---------|*log(27)|
           |               | 3         \x                 /                           2          x              \x                 / |   2                         x    ||                  \x                 /         |   2       \x                 /                          x    |        |
           \               \x                                                        x                                               \  x                               //                                               \  x                                                           /        /

$$27^{x} x^{27^{x}} \left(3 \cdot 27^{x} \left(\log{\left(27 \right)} \log{\left(x \right)} + \frac{1}{x}\right) \log{\left(27 \right)}^{2} + 3 \cdot 27^{x} \left(27^{x} \left(\log{\left(27 \right)} \log{\left(x \right)} + \frac{1}{x}\right)^{2} + \log{\left(27 \right)}^{2} \log{\left(x \right)} + \frac{2 \log{\left(27 \right)}}{x} - \frac{1}{x^{2}}\right) \log{\left(27 \right)} + 27^{x} \left(27^{2 x} \left(\log{\left(27 \right)} \log{\left(x \right)} + \frac{1}{x}\right)^{3} + 3 \cdot 27^{x} \left(\log{\left(27 \right)} \log{\left(x \right)} + \frac{1}{x}\right) \left(\log{\left(27 \right)}^{2} \log{\left(x \right)} + \frac{2 \log{\left(27 \right)}}{x} - \frac{1}{x^{2}}\right) + \log{\left(27 \right)}^{3} \log{\left(x \right)} + \frac{3 \log{\left(27 \right)}^{2}}{x} - \frac{3 \log{\left(27 \right)}}{x^{2}} + \frac{2}{x^{3}}\right) + \log{\left(27 \right)}^{3}\right)$$

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Derivada de x^(27^x)*27^x

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