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(x/sqrt(1-x))^x^2

Derivada de (x/sqrt(1-x))^x^2

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src]
           / 2\
           \x /
/    x    \    
|---------|    
|  _______|    
\\/ 1 - x /    
$$\left(\frac{x}{\sqrt{1 - x}}\right)^{x^{2}}$$
(x/sqrt(1 - x))^(x^2)
Solución detallada
  1. No logro encontrar los pasos en la búsqueda de esta derivada.

    Perola derivada


Respuesta:

Gráfica
Primera derivada [src]
           / 2\                                                              
           \x /                                                              
/    x    \     /       /    x    \       _______ /    1            x      \\
|---------|    *|2*x*log|---------| + x*\/ 1 - x *|--------- + ------------||
|  _______|     |       |  _______|               |  _______            3/2||
\\/ 1 - x /     \       \\/ 1 - x /               \\/ 1 - x    2*(1 - x)   //
$$\left(\frac{x}{\sqrt{1 - x}}\right)^{x^{2}} \left(x \sqrt{1 - x} \left(\frac{x}{2 \left(1 - x\right)^{\frac{3}{2}}} + \frac{1}{\sqrt{1 - x}}\right) + 2 x \log{\left(\frac{x}{\sqrt{1 - x}} \right)}\right)$$
Segunda derivada [src]
                /                                                                                          2                            \
                |                         /    2        2       3*x   \    2 /         /    x    \     x  \                             |
           / 2\ |                       x*|- ------ + ----- + --------|   x *|2 + 4*log|---------| + -----|                  /      x  \|
           \x / |                         |  -1 + x   1 - x          2|      |         |  _______|   1 - x|                x*|2 + -----||
/    x    \     |         /    x    \     \                   (1 - x) /      \         \\/ 1 - x /        /       3*x        \    1 - x/|
|---------|    *|3 + 2*log|---------| + ------------------------------- + ---------------------------------- + --------- - -------------|
|  _______|     |         |  _______|                  4                                  4                    2*(1 - x)     4*(1 - x)  |
\\/ 1 - x /     \         \\/ 1 - x /                                                                                                   /
$$\left(\frac{x}{\sqrt{1 - x}}\right)^{x^{2}} \left(\frac{x^{2} \left(\frac{x}{1 - x} + 4 \log{\left(\frac{x}{\sqrt{1 - x}} \right)} + 2\right)^{2}}{4} + \frac{x \left(\frac{3 x}{\left(1 - x\right)^{2}} - \frac{2}{x - 1} + \frac{2}{1 - x}\right)}{4} - \frac{x \left(\frac{x}{1 - x} + 2\right)}{4 \left(1 - x\right)} + \frac{3 x}{2 \left(1 - x\right)} + 2 \log{\left(\frac{x}{\sqrt{1 - x}} \right)} + 3\right)$$
Tercera derivada [src]
                /                                                                                                                                                                                                  /                                                                    /      x  \\\
                |                                                                                       3                                                                                                          |                                                                  x*|2 + -----|||
                |                                                       3 /         /    x    \     x  \      /    2        2       3*x   \                                         /         /    x    \     x  \ |          /    x    \     /    2        2       3*x   \    6*x      \    1 - x/||
           / 2\ |                         x           x                x *|2 + 4*log|---------| + -----|    x*|- ------ + ----- + --------|     /      x  \       /     5*x \   3*x*|2 + 4*log|---------| + -----|*|12 + 8*log|---------| + x*|- ------ + ----- + --------| + ----- - -------------||
           \x / |                   2 + -----   2 + -----                 |         |  _______|   1 - x|      |  -1 + x   1 - x          2|   x*|2 + -----|   3*x*|6 + -----|       |         |  _______|   1 - x| |          |  _______|     |  -1 + x   1 - x          2|   1 - x       1 - x    ||
/    x    \     |    2        2         1 - x       1 - x     3*x         \         \\/ 1 - x /        /      \                   (1 - x) /     \    1 - x/       \    1 - x/       \         \\/ 1 - x /        / \          \\/ 1 - x /     \                   (1 - x) /                        /|
|---------|    *|- ------ + ----- + --------- - --------- + -------- + ---------------------------------- - ------------------------------- - ------------- + --------------- + --------------------------------------------------------------------------------------------------------------------|
|  _______|     |  -1 + x   1 - x       x         1 - x            2                   8                               4*(1 - x)                         2                2                                                              8                                                          |
\\/ 1 - x /     \                                           (1 - x)                                                                             8*(1 - x)        8*(1 - x)                                                                                                                          /
$$\left(\frac{x}{\sqrt{1 - x}}\right)^{x^{2}} \left(\frac{x^{3} \left(\frac{x}{1 - x} + 4 \log{\left(\frac{x}{\sqrt{1 - x}} \right)} + 2\right)^{3}}{8} + \frac{3 x \left(\frac{x}{1 - x} + 4 \log{\left(\frac{x}{\sqrt{1 - x}} \right)} + 2\right) \left(x \left(\frac{3 x}{\left(1 - x\right)^{2}} - \frac{2}{x - 1} + \frac{2}{1 - x}\right) - \frac{x \left(\frac{x}{1 - x} + 2\right)}{1 - x} + \frac{6 x}{1 - x} + 8 \log{\left(\frac{x}{\sqrt{1 - x}} \right)} + 12\right)}{8} - \frac{x \left(\frac{3 x}{\left(1 - x\right)^{2}} - \frac{2}{x - 1} + \frac{2}{1 - x}\right)}{4 \left(1 - x\right)} - \frac{x \left(\frac{x}{1 - x} + 2\right)}{8 \left(1 - x\right)^{2}} + \frac{3 x \left(\frac{5 x}{1 - x} + 6\right)}{8 \left(1 - x\right)^{2}} + \frac{3 x}{\left(1 - x\right)^{2}} - \frac{2}{x - 1} - \frac{\frac{x}{1 - x} + 2}{1 - x} + \frac{2}{1 - x} + \frac{\frac{x}{1 - x} + 2}{x}\right)$$
Gráfico
Derivada de (x/sqrt(1-x))^x^2