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(xe)^x
Derivada de la función/ (xe)^x

Derivada de (xe)^x

Función f() - derivada -er orden en el punto
v

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
     x
(x*E)
(ex)x\left(e x\right)^{x} 
(x*E)^x
Solución detallada

  1. No logro encontrar los pasos en la búsqueda de esta derivada.

    Perola derivada

    xx(log⁡(x)+1)x^{x} \left(\log{\left(x \right)} + 1\right)

Respuesta:

xx(log⁡(x)+1)x^{x} \left(\log{\left(x \right)} + 1\right)

Gráfica
02468-8-6-4-2-1010-10000000000000001000000000000000
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Primera derivada [src] 
     x               
(x*E) *(1 + log(x*E))
(ex)x(log⁡(ex)+1)\left(e x\right)^{x} \left(\log{\left(e x \right)} + 1\right)
Simplificar
Segunda derivada [src] 
     x /1                 2\
(E*x) *|- + (1 + log(E*x)) |
       \x                  /
(ex)x((log⁡(ex)+1)2+1x)\left(e x\right)^{x} \left(\left(\log{\left(e x \right)} + 1\right)^{2} + \frac{1}{x}\right)
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Tercera derivada [src] 
     x /              3   1    3*(1 + log(E*x))\
(E*x) *|(1 + log(E*x))  - -- + ----------------|
       |                   2          x        |
       \                  x                    /
(ex)x((log⁡(ex)+1)3+3(log⁡(ex)+1)x−1x2)\left(e x\right)^{x} \left(\left(\log{\left(e x \right)} + 1\right)^{3} + \frac{3 \left(\log{\left(e x \right)} + 1\right)}{x} - \frac{1}{x^{2}}\right)
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10-я производная [src] 
       /                                                                                                                                                  3                       3                                              3                      5                      5                     7                    8                     6                     6                      4                      2                      4                      4                       2                       2                       2\
     x |              10   945   12600   40320   40740   61416   78480*(1 + log(E*x))   50680*(1 + log(E*x))   50400*(1 + log(E*x))   23520*(1 + log(E*x))    14400*(1 + log(E*x))    12600*(1 + log(E*x))   12600*(1 + log(E*x))    2520*(1 + log(E*x))    1512*(1 + log(E*x))    120*(1 + log(E*x))    45*(1 + log(E*x))    420*(1 + log(E*x))    630*(1 + log(E*x))    3150*(1 + log(E*x))    4725*(1 + log(E*x))    5040*(1 + log(E*x))    8400*(1 + log(E*x))    31500*(1 + log(E*x))    32400*(1 + log(E*x))    51660*(1 + log(E*x)) |
(E*x) *|(1 + log(E*x))   + --- + ----- + ----- + ----- + ----- - -------------------- - -------------------- - -------------------- - --------------------- - --------------------- - -------------------- - --------------------- - -------------------- - -------------------- - ------------------- + ------------------ + ------------------- + ------------------- + -------------------- + -------------------- + -------------------- + -------------------- + --------------------- + --------------------- + ---------------------|
       |                     5      6       9       7       8              7                      6                      8                       5                       6                      5                       4                      3                      4                      2                   x                      3                     2                     3                      4                      5                      4                       5                       7                       6         |
       \                    x      x       x       x       x              x                      x                      x                       x                       x                      x                       x                      x                      x                      x                                          x                     x                     x                      x                      x                      x                       x                       x                       x          /
(ex)x((log⁡(ex)+1)10+45(log⁡(ex)+1)8x−120(log⁡(ex)+1)7x2+630(log⁡(ex)+1)6x2+420(log⁡(ex)+1)6x3−2520(log⁡(ex)+1)5x3+3150(log⁡(ex)+1)4x3−1512(log⁡(ex)+1)5x4+8400(log⁡(ex)+1)4x4−12600(log⁡(ex)+1)3x4+4725(log⁡(ex)+1)2x4+5040(log⁡(ex)+1)4x5−23520(log⁡(ex)+1)3x5+31500(log⁡(ex)+1)2x5−12600(log⁡(ex)+1)x5+945x5−14400(log⁡(ex)+1)3x6+51660(log⁡(ex)+1)2x6−50680(log⁡(ex)+1)x6+12600x6+32400(log⁡(ex)+1)2x7−78480(log⁡(ex)+1)x7+40740x7−50400(log⁡(ex)+1)x8+61416x8+40320x9)\left(e x\right)^{x} \left(\left(\log{\left(e x \right)} + 1\right)^{10} + \frac{45 \left(\log{\left(e x \right)} + 1\right)^{8}}{x} - \frac{120 \left(\log{\left(e x \right)} + 1\right)^{7}}{x^{2}} + \frac{630 \left(\log{\left(e x \right)} + 1\right)^{6}}{x^{2}} + \frac{420 \left(\log{\left(e x \right)} + 1\right)^{6}}{x^{3}} - \frac{2520 \left(\log{\left(e x \right)} + 1\right)^{5}}{x^{3}} + \frac{3150 \left(\log{\left(e x \right)} + 1\right)^{4}}{x^{3}} - \frac{1512 \left(\log{\left(e x \right)} + 1\right)^{5}}{x^{4}} + \frac{8400 \left(\log{\left(e x \right)} + 1\right)^{4}}{x^{4}} - \frac{12600 \left(\log{\left(e x \right)} + 1\right)^{3}}{x^{4}} + \frac{4725 \left(\log{\left(e x \right)} + 1\right)^{2}}{x^{4}} + \frac{5040 \left(\log{\left(e x \right)} + 1\right)^{4}}{x^{5}} - \frac{23520 \left(\log{\left(e x \right)} + 1\right)^{3}}{x^{5}} + \frac{31500 \left(\log{\left(e x \right)} + 1\right)^{2}}{x^{5}} - \frac{12600 \left(\log{\left(e x \right)} + 1\right)}{x^{5}} + \frac{945}{x^{5}} - \frac{14400 \left(\log{\left(e x \right)} + 1\right)^{3}}{x^{6}} + \frac{51660 \left(\log{\left(e x \right)} + 1\right)^{2}}{x^{6}} - \frac{50680 \left(\log{\left(e x \right)} + 1\right)}{x^{6}} + \frac{12600}{x^{6}} + \frac{32400 \left(\log{\left(e x \right)} + 1\right)^{2}}{x^{7}} - \frac{78480 \left(\log{\left(e x \right)} + 1\right)}{x^{7}} + \frac{40740}{x^{7}} - \frac{50400 \left(\log{\left(e x \right)} + 1\right)}{x^{8}} + \frac{61416}{x^{8}} + \frac{40320}{x^{9}}\right)
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Gráfico
Derivada de (xe)^x
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