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(x/(x+2))^(x^2)
Derivada de la función/ (x^2)/ (x+2)/ (x/(x+2))^(x^2)

Derivada de (x/(x+2))^(x^2)

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

Gráfico:

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Solución

Ha introducido [src] 
       / 2\
       \x /
/  x  \    
|-----|    
\x + 2/
(xx+2)x2\left(\frac{x}{x + 2}\right)^{x^{2}} 
(x/(x + 2))^(x^2)
Solución detallada

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

    Perola derivada

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

Respuesta:

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

Gráfica
02468-8-6-4-2-1010-2000000000020000000000
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Trazar el gráfico f'(x)
Primera derivada [src] 
       / 2\                                                
       \x /                                                
/  x  \     /       /  x  \             /  1        x    \\
|-----|    *|2*x*log|-----| + x*(x + 2)*|----- - --------||
\x + 2/     |       \x + 2/             |x + 2          2||
            \                           \        (x + 2) //
(xx+2)x2(x(x+2)(−x(x+2)2+1x+2)+2xlog⁡(xx+2))\left(\frac{x}{x + 2}\right)^{x^{2}} \left(x \left(x + 2\right) \left(- \frac{x}{\left(x + 2\right)^{2}} + \frac{1}{x + 2}\right) + 2 x \log{\left(\frac{x}{x + 2} \right)}\right)
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Segunda derivada [src] 
       / 2\ /                                                               /       x  \\
       \x / |                                                 2           x*|-1 + -----||
/  x  \     |         /  x  \    2 /          /  x  \     x  \     3*x      \     2 + x/|
|-----|    *|3 + 2*log|-----| + x *|-1 - 2*log|-----| + -----|  - ----- + --------------|
\2 + x/     \         \2 + x/      \          \2 + x/   2 + x/    2 + x       2 + x     /
(xx+2)x2(x2(xx+2−2log⁡(xx+2)−1)2+x(xx+2−1)x+2−3xx+2+2log⁡(xx+2)+3)\left(\frac{x}{x + 2}\right)^{x^{2}} \left(x^{2} \left(\frac{x}{x + 2} - 2 \log{\left(\frac{x}{x + 2} \right)} - 1\right)^{2} + \frac{x \left(\frac{x}{x + 2} - 1\right)}{x + 2} - \frac{3 x}{x + 2} + 2 \log{\left(\frac{x}{x + 2} \right)} + 3\right)
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Tercera derivada [src] 
       / 2\ /                                                       /       x  \     /       x  \                                   /                             /       x  \\       /       x  \\
       \x / |                                      3              2*|-1 + -----|   8*|-1 + -----|                                   |                           x*|-1 + -----||   2*x*|-1 + -----||
/  x  \     |  4      3 /          /  x  \     x  \      4*x        \     2 + x/     \     2 + x/       /          /  x  \     x  \ |         /  x  \    3*x      \     2 + x/|       \     2 + x/|
|-----|    *|----- - x *|-1 - 2*log|-----| + -----|  - -------- - -------------- + -------------- - 3*x*|-1 - 2*log|-----| + -----|*|3 + 2*log|-----| - ----- + --------------| - ----------------|
\2 + x/     |2 + x      \          \2 + x/   2 + x/           2         x              2 + x            \          \2 + x/   2 + x/ \         \2 + x/   2 + x       2 + x     /              2    |
            \                                          (2 + x)                                                                                                                        (2 + x)     /
(xx+2)x2(−x3(xx+2−2log⁡(xx+2)−1)3−3x(xx+2−2log⁡(xx+2)−1)(x(xx+2−1)x+2−3xx+2+2log⁡(xx+2)+3)−2x(xx+2−1)(x+2)2−4x(x+2)2+8(xx+2−1)x+2+4x+2−2(xx+2−1)x)\left(\frac{x}{x + 2}\right)^{x^{2}} \left(- x^{3} \left(\frac{x}{x + 2} - 2 \log{\left(\frac{x}{x + 2} \right)} - 1\right)^{3} - 3 x \left(\frac{x}{x + 2} - 2 \log{\left(\frac{x}{x + 2} \right)} - 1\right) \left(\frac{x \left(\frac{x}{x + 2} - 1\right)}{x + 2} - \frac{3 x}{x + 2} + 2 \log{\left(\frac{x}{x + 2} \right)} + 3\right) - \frac{2 x \left(\frac{x}{x + 2} - 1\right)}{\left(x + 2\right)^{2}} - \frac{4 x}{\left(x + 2\right)^{2}} + \frac{8 \left(\frac{x}{x + 2} - 1\right)}{x + 2} + \frac{4}{x + 2} - \frac{2 \left(\frac{x}{x + 2} - 1\right)}{x}\right)
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Gráfico
Derivada de (x/(x+2))^(x^2)
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