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Derivada de y=(1-x^2)^(5-4x^3)

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Solución

Ha introducido [src]
               3
        5 - 4*x 
/     2\        
\1 - x /        
$$\left(1 - x^{2}\right)^{5 - 4 x^{3}}$$
(1 - x^2)^(5 - 4*x^3)
Solución detallada
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Respuesta:

Primera derivada [src]
               3                                       
        5 - 4*x  /                          /       3\\
/     2\         |      2    /     2\   2*x*\5 - 4*x /|
\1 - x /        *|- 12*x *log\1 - x / - --------------|
                 |                               2    |
                 \                          1 - x     /
$$\left(1 - x^{2}\right)^{5 - 4 x^{3}} \left(- 12 x^{2} \log{\left(1 - x^{2} \right)} - \frac{2 x \left(5 - 4 x^{3}\right)}{1 - x^{2}}\right)$$
Segunda derivada [src]
                 3 /                                                                             2                   \
          5 - 4*x  |          3        3                            /        3                  \       2 /        3\|
  /     2\         |  -5 + 4*x     24*x             /     2\      2 |-5 + 4*x           /     2\|    2*x *\-5 + 4*x /|
2*\1 - x /        *|- --------- - ------- - 12*x*log\1 - x / + 2*x *|--------- + 6*x*log\1 - x /|  + ----------------|
                   |         2          2                           |       2                   |                2   |
                   |   -1 + x     -1 + x                            \ -1 + x                    /       /      2\    |
                   \                                                                                    \-1 + x /    /
$$2 \left(1 - x^{2}\right)^{5 - 4 x^{3}} \left(- \frac{24 x^{3}}{x^{2} - 1} + 2 x^{2} \left(6 x \log{\left(1 - x^{2} \right)} + \frac{4 x^{3} - 5}{x^{2} - 1}\right)^{2} + \frac{2 x^{2} \left(4 x^{3} - 5\right)}{\left(x^{2} - 1\right)^{2}} - 12 x \log{\left(1 - x^{2} \right)} - \frac{4 x^{3} - 5}{x^{2} - 1}\right)$$
Tercera derivada [src]
                 3 /                                                              3                                                                                                                                                  \
          5 - 4*x  |                       2         /        3                  \          4         3 /        3\       /        3\       /        3                  \ /        3                           3       2 /        3\\|
  /     2\         |       /     2\    54*x        3 |-5 + 4*x           /     2\|      36*x       4*x *\-5 + 4*x /   3*x*\-5 + 4*x /       |-5 + 4*x           /     2\| |-5 + 4*x            /     2\    24*x     2*x *\-5 + 4*x /||
4*\1 - x /        *|- 6*log\1 - x / - ------- - 2*x *|--------- + 6*x*log\1 - x /|  + ---------- - ---------------- + --------------- + 3*x*|--------- + 6*x*log\1 - x /|*|--------- + 12*x*log\1 - x / + ------- - ----------------||
                   |                        2        |       2                   |             2               3                  2         |       2                   | |       2                             2               2   ||
                   |                  -1 + x         \ -1 + x                    /    /      2\       /      2\          /      2\          \ -1 + x                    / | -1 + x                        -1 + x       /      2\    ||
                   \                                                                  \-1 + x /       \-1 + x /          \-1 + x /                                        \                                            \-1 + x /    //
$$4 \left(1 - x^{2}\right)^{5 - 4 x^{3}} \left(\frac{36 x^{4}}{\left(x^{2} - 1\right)^{2}} - 2 x^{3} \left(6 x \log{\left(1 - x^{2} \right)} + \frac{4 x^{3} - 5}{x^{2} - 1}\right)^{3} - \frac{4 x^{3} \left(4 x^{3} - 5\right)}{\left(x^{2} - 1\right)^{3}} - \frac{54 x^{2}}{x^{2} - 1} + 3 x \left(6 x \log{\left(1 - x^{2} \right)} + \frac{4 x^{3} - 5}{x^{2} - 1}\right) \left(\frac{24 x^{3}}{x^{2} - 1} - \frac{2 x^{2} \left(4 x^{3} - 5\right)}{\left(x^{2} - 1\right)^{2}} + 12 x \log{\left(1 - x^{2} \right)} + \frac{4 x^{3} - 5}{x^{2} - 1}\right) + \frac{3 x \left(4 x^{3} - 5\right)}{\left(x^{2} - 1\right)^{2}} - 6 \log{\left(1 - x^{2} \right)}\right)$$