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(x-lnx)^(2-x)
Derivada de la función/ x-lnx/ (2-x)/ (x-lnx)^(2-x)

Derivada de (x-lnx)^(2-x)

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

Gráfico:

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Solución

Ha introducido [src] 
            2 - x
(x - log(x))
(x−log⁡(x))2−x\left(x - \log{\left(x \right)}\right)^{2 - x} 
(x - log(x))^(2 - x)
Solución detallada

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

    Perola derivada

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

Respuesta:

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

Gráfica
02468-8-6-4-2-1010-5050
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
                  /                   /    1\        \
                  |                   |1 - -|*(2 - x)|
            2 - x |                   \    x/        |
(x - log(x))     *|-log(x - log(x)) + ---------------|
                  \                      x - log(x)  /
(x−log⁡(x))2−x((1−1x)(2−x)x−log⁡(x)−log⁡(x−log⁡(x)))\left(x - \log{\left(x \right)}\right)^{2 - x} \left(\frac{\left(1 - \frac{1}{x}\right) \left(2 - x\right)}{x - \log{\left(x \right)}} - \log{\left(x - \log{\left(x \right)} \right)}\right)
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Segunda derivada [src] 
                  /                                                                2         \
                  |                                                         /    1\          |
                  |                                                         |1 - -| *(-2 + x)|
                  |                                    2       2   -2 + x   \    x/          |
                  |//    1\                           \    2 - - + ------ - -----------------|
                  |||1 - -|*(-2 + x)                  |        x      2         x - log(x)   |
            2 - x ||\    x/                           |              x                       |
(x - log(x))     *||---------------- + log(x - log(x))|  - ----------------------------------|
                  \\   x - log(x)                     /                x - log(x)            /
(x−log⁡(x))2−x(((1−1x)(x−2)x−log⁡(x)+log⁡(x−log⁡(x)))2−−(1−1x)2(x−2)x−log⁡(x)+2−2x+x−2x2x−log⁡(x))\left(x - \log{\left(x \right)}\right)^{2 - x} \left(\left(\frac{\left(1 - \frac{1}{x}\right) \left(x - 2\right)}{x - \log{\left(x \right)}} + \log{\left(x - \log{\left(x \right)} \right)}\right)^{2} - \frac{- \frac{\left(1 - \frac{1}{x}\right)^{2} \left(x - 2\right)}{x - \log{\left(x \right)}} + 2 - \frac{2}{x} + \frac{x - 2}{x^{2}}}{x - \log{\left(x \right)}}\right)
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Tercera derivada [src] 
                  /                                                                       2            3                                                                        /                        2         \\
                  |                                                                /    1\      /    1\               /    1\              //    1\                           \ |                 /    1\          ||
                  |                                                              3*|1 - -|    2*|1 - -| *(-2 + x)   3*|1 - -|*(-2 + x)     ||1 - -|*(-2 + x)                  | |                 |1 - -| *(-2 + x)||
                  |                                      3     3    2*(-2 + x)     \    x/      \    x/               \    x/              |\    x/                           | |    2   -2 + x   \    x/          ||
                  |  //    1\                           \    - -- + ---------- + ---------- - ------------------- + ------------------   3*|---------------- + log(x - log(x))|*|2 - - + ------ - -----------------||
                  |  ||1 - -|*(-2 + x)                  |       2        3       x - log(x)                  2        2                    \   x - log(x)                     / |    x      2         x - log(x)   ||
            2 - x |  |\    x/                           |      x        x                        (x - log(x))        x *(x - log(x))                                            \          x                       /|
(x - log(x))     *|- |---------------- + log(x - log(x))|  + ------------------------------------------------------------------------- + ---------------------------------------------------------------------------|
                  \  \   x - log(x)                     /                                    x - log(x)                                                                   x - log(x)                                /
(x−log⁡(x))2−x(−((1−1x)(x−2)x−log⁡(x)+log⁡(x−log⁡(x)))3+3((1−1x)(x−2)x−log⁡(x)+log⁡(x−log⁡(x)))(−(1−1x)2(x−2)x−log⁡(x)+2−2x+x−2x2)x−log⁡(x)+−2(1−1x)3(x−2)(x−log⁡(x))2+3(1−1x)2x−log⁡(x)+3(1−1x)(x−2)x2(x−log⁡(x))−3x2+2(x−2)x3x−log⁡(x))\left(x - \log{\left(x \right)}\right)^{2 - x} \left(- \left(\frac{\left(1 - \frac{1}{x}\right) \left(x - 2\right)}{x - \log{\left(x \right)}} + \log{\left(x - \log{\left(x \right)} \right)}\right)^{3} + \frac{3 \left(\frac{\left(1 - \frac{1}{x}\right) \left(x - 2\right)}{x - \log{\left(x \right)}} + \log{\left(x - \log{\left(x \right)} \right)}\right) \left(- \frac{\left(1 - \frac{1}{x}\right)^{2} \left(x - 2\right)}{x - \log{\left(x \right)}} + 2 - \frac{2}{x} + \frac{x - 2}{x^{2}}\right)}{x - \log{\left(x \right)}} + \frac{- \frac{2 \left(1 - \frac{1}{x}\right)^{3} \left(x - 2\right)}{\left(x - \log{\left(x \right)}\right)^{2}} + \frac{3 \left(1 - \frac{1}{x}\right)^{2}}{x - \log{\left(x \right)}} + \frac{3 \left(1 - \frac{1}{x}\right) \left(x - 2\right)}{x^{2} \left(x - \log{\left(x \right)}\right)} - \frac{3}{x^{2}} + \frac{2 \left(x - 2\right)}{x^{3}}}{x - \log{\left(x \right)}}\right)
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Gráfico
Derivada de (x-lnx)^(2-x)
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