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

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

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

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Solución

Ha introducido [src] 
 x*x*x + 2*x
x
xxxx+2xx^{x x x + 2 x} 
x^((x*x)*x + 2*x)
Solución detallada

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

    Perola derivada

    (xxx+2x)xxx+2x(log⁡(xxx+2x)+1)\left(x x x + 2 x\right)^{x x x + 2 x} \left(\log{\left(x x x + 2 x \right)} + 1\right)

  2. Simplificamos:

    (x(x2+2))x(x2+2)(log⁡(x(x2+2))+1)\left(x \left(x^{2} + 2\right)\right)^{x \left(x^{2} + 2\right)} \left(\log{\left(x \left(x^{2} + 2\right) \right)} + 1\right)

Respuesta:

(x(x2+2))x(x2+2)(log⁡(x(x2+2))+1)\left(x \left(x^{2} + 2\right)\right)^{x \left(x^{2} + 2\right)} \left(\log{\left(x \left(x^{2} + 2\right) \right)} + 1\right)

Primera derivada [src] 
 x*x*x + 2*x /x*x*x + 2*x   /       2      \       \
x           *|----------- + \2 + 2*x  + x*x/*log(x)|
             \     x                               /
xxxx+2x((2x2+xx+2)log⁡(x)+xxx+2xx)x^{x x x + 2 x} \left(\left(2 x^{2} + x x + 2\right) \log{\left(x \right)} + \frac{x x x + 2 x}{x}\right)
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Segunda derivada [src] 
   /     2\ /                            2        2     /       2\             \
 x*\2 + x / |/     2   /       2\       \    2 + x    2*\2 + 3*x /             |
x          *|\2 + x  + \2 + 3*x /*log(x)/  - ------ + ------------ + 6*x*log(x)|
            \                                  x           x                   /
xx(x2+2)(6xlog⁡(x)+(x2+(3x2+2)log⁡(x)+2)2−x2+2x+2(3x2+2)x)x^{x \left(x^{2} + 2\right)} \left(6 x \log{\left(x \right)} + \left(x^{2} + \left(3 x^{2} + 2\right) \log{\left(x \right)} + 2\right)^{2} - \frac{x^{2} + 2}{x} + \frac{2 \left(3 x^{2} + 2\right)}{x}\right)
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Tercera derivada [src] 
   /     2\ /                                 3                /       2\     /     2\                                  /       2     /       2\             \\
 x*\2 + x / |     /     2   /       2\       \               3*\2 + 3*x /   2*\2 + x /     /     2   /       2\       \ |  2 + x    2*\2 + 3*x /             ||
x          *|18 + \2 + x  + \2 + 3*x /*log(x)/  + 6*log(x) - ------------ + ---------- + 3*\2 + x  + \2 + 3*x /*log(x)/*|- ------ + ------------ + 6*x*log(x)||
            |                                                      2             2                                      \    x           x                   /|
            \                                                     x             x                                                                             /
xx(x2+2)((x2+(3x2+2)log⁡(x)+2)3+3(x2+(3x2+2)log⁡(x)+2)(6xlog⁡(x)−x2+2x+2(3x2+2)x)+6log⁡(x)+18+2(x2+2)x2−3(3x2+2)x2)x^{x \left(x^{2} + 2\right)} \left(\left(x^{2} + \left(3 x^{2} + 2\right) \log{\left(x \right)} + 2\right)^{3} + 3 \left(x^{2} + \left(3 x^{2} + 2\right) \log{\left(x \right)} + 2\right) \left(6 x \log{\left(x \right)} - \frac{x^{2} + 2}{x} + \frac{2 \left(3 x^{2} + 2\right)}{x}\right) + 6 \log{\left(x \right)} + 18 + \frac{2 \left(x^{2} + 2\right)}{x^{2}} - \frac{3 \left(3 x^{2} + 2\right)}{x^{2}}\right)
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