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x^((3/(1-x))^2)
Derivada de la función/ (1-x)/ x^((3/(1-x))^2)

Derivada de x^((3/(1-x))^2)

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

Ha introducido [src] 
 /       2\
 |/  3  \ |
 ||-----| |
 \\1 - x/ /
x
x(31−x)2x^{\left(\frac{3}{1 - x}\right)^{2}} 
x^((3/(1 - x))^2)
Solución detallada

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

    Perola derivada

    (log⁡((31−x)2)+1)((31−x)2)(31−x)2\left(\log{\left(\left(\frac{3}{1 - x}\right)^{2} \right)} + 1\right) \left(\left(\frac{3}{1 - x}\right)^{2}\right)^{\left(\frac{3}{1 - x}\right)^{2}}

  2. Simplificamos:

    (387420489(x−1)18)1(x−1)2(log⁡(9(x−1)2)+1)\left(\frac{387420489}{\left(x - 1\right)^{18}}\right)^{\frac{1}{\left(x - 1\right)^{2}}} \left(\log{\left(\frac{9}{\left(x - 1\right)^{2}} \right)} + 1\right)

Respuesta:

(387420489(x−1)18)1(x−1)2(log⁡(9(x−1)2)+1)\left(\frac{387420489}{\left(x - 1\right)^{18}}\right)^{\frac{1}{\left(x - 1\right)^{2}}} \left(\log{\left(\frac{9}{\left(x - 1\right)^{2}} \right)} + 1\right)

Gráfica
02468-8-6-4-2-1010-2e362e36
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Primera derivada [src] 
 /       2\ //   9    \                    \
 |/  3  \ | ||--------|      /1   x\       |
 ||-----| | ||       2|   54*|- - -|*log(x)|
 \\1 - x/ / |\(1 - x) /      \3   3/       |
x          *|---------- + -----------------|
            |    x                    4    |
            \                  (1 - x)     /
x(31−x)2(54(13−x3)log⁡(x)(1−x)4+91(1−x)2x)x^{\left(\frac{3}{1 - x}\right)^{2}} \left(\frac{54 \left(\frac{1}{3} - \frac{x}{3}\right) \log{\left(x \right)}}{\left(1 - x\right)^{4}} + \frac{9 \frac{1}{\left(1 - x\right)^{2}}}{x}\right)
Simplificar
Segunda derivada [src] 
       9     /                                                  2\
   --------- |                                  /  1   2*log(x)\ |
           2 |                                9*|- - + --------| |
   (-1 + x)  |  1        4         6*log(x)     \  x    -1 + x / |
9*x         *|- -- - ---------- + --------- + -------------------|
             |   2   x*(-1 + x)           2                2     |
             \  x                 (-1 + x)         (-1 + x)      /
------------------------------------------------------------------
                                    2                             
                            (-1 + x)
9x9(x−1)2(9(2log⁡(x)x−1−1x)2(x−1)2+6log⁡(x)(x−1)2−4x(x−1)−1x2)(x−1)2\frac{9 x^{\frac{9}{\left(x - 1\right)^{2}}} \left(\frac{9 \left(\frac{2 \log{\left(x \right)}}{x - 1} - \frac{1}{x}\right)^{2}}{\left(x - 1\right)^{2}} + \frac{6 \log{\left(x \right)}}{\left(x - 1\right)^{2}} - \frac{4}{x \left(x - 1\right)} - \frac{1}{x^{2}}\right)}{\left(x - 1\right)^{2}}
Simplificar
Tercera derivada [src] 
       9     /                        3                                              /  1   2*log(x)\ /1     6*log(x)       4     \\
   --------- |        /  1   2*log(x)\                                            27*|- - + --------|*|-- - --------- + ----------||
           2 |     81*|- - + --------|                                               \  x    -1 + x / | 2           2   x*(-1 + x)||
   (-1 + x)  |2       \  x    -1 + x /    24*log(x)        6             18                           \x    (-1 + x)              /|
9*x         *|-- - -------------------- - --------- + ----------- + ----------- + -------------------------------------------------|
             | 3                4                 3    2                      2                               2                    |
             \x         (-1 + x)          (-1 + x)    x *(-1 + x)   x*(-1 + x)                        (-1 + x)                     /
------------------------------------------------------------------------------------------------------------------------------------
                                                                     2                                                              
                                                             (-1 + x)
9x9(x−1)2(27(2log⁡(x)x−1−1x)(−6log⁡(x)(x−1)2+4x(x−1)+1x2)(x−1)2−24log⁡(x)(x−1)3−81(2log⁡(x)x−1−1x)3(x−1)4+18x(x−1)2+6x2(x−1)+2x3)(x−1)2\frac{9 x^{\frac{9}{\left(x - 1\right)^{2}}} \left(\frac{27 \left(\frac{2 \log{\left(x \right)}}{x - 1} - \frac{1}{x}\right) \left(- \frac{6 \log{\left(x \right)}}{\left(x - 1\right)^{2}} + \frac{4}{x \left(x - 1\right)} + \frac{1}{x^{2}}\right)}{\left(x - 1\right)^{2}} - \frac{24 \log{\left(x \right)}}{\left(x - 1\right)^{3}} - \frac{81 \left(\frac{2 \log{\left(x \right)}}{x - 1} - \frac{1}{x}\right)^{3}}{\left(x - 1\right)^{4}} + \frac{18}{x \left(x - 1\right)^{2}} + \frac{6}{x^{2} \left(x - 1\right)} + \frac{2}{x^{3}}\right)}{\left(x - 1\right)^{2}}
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Gráfico
Derivada de x^((3/(1-x))^2)
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