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y=5ln*arcsinx
Derivada de la función/ arcsin/ y=5ln*arcsinx

Derivada de y=5ln*arcsinx

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

Ha introducido [src] 
5*log(x)*asin(x)
5log⁡(x)asin⁡(x)5 \log{\left(x \right)} \operatorname{asin}{\left(x \right)} 
(5*log(x))*asin(x)
Gráfica
02468-8-6-4-2-1010-1010
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Trazar el gráfico f'(x)
Primera derivada [src] 
5*asin(x)     5*log(x) 
--------- + -----------
    x          ________
              /      2 
            \/  1 - x
5log⁡(x)1−x2+5asin⁡(x)x\frac{5 \log{\left(x \right)}}{\sqrt{1 - x^{2}}} + \frac{5 \operatorname{asin}{\left(x \right)}}{x}
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Segunda derivada [src] 
  /  asin(x)         2           x*log(x) \
5*|- ------- + ------------- + -----------|
  |      2          ________           3/2|
  |     x          /      2    /     2\   |
  \            x*\/  1 - x     \1 - x /   /
5(xlog⁡(x)(1−x2)32+2x1−x2−asin⁡(x)x2)5 \left(\frac{x \log{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{2}{x \sqrt{1 - x^{2}}} - \frac{\operatorname{asin}{\left(x \right)}}{x^{2}}\right)
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Tercera derivada [src] 
  /                                           /          2 \       \
  |                                           |       3*x  |       |
  |                                           |-1 + -------|*log(x)|
  |                                           |           2|       |
  |     3              3          2*asin(x)   \     -1 + x /       |
5*|----------- - -------------- + --------- - ---------------------|
  |        3/2         ________        3                   3/2     |
  |/     2\       2   /      2        x            /     2\        |
  \\1 - x /      x *\/  1 - x                      \1 - x /        /
5(−(3x2x2−1−1)log⁡(x)(1−x2)32+3(1−x2)32−3x21−x2+2asin⁡(x)x3)5 \left(- \frac{\left(\frac{3 x^{2}}{x^{2} - 1} - 1\right) \log{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{3}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{3}{x^{2} \sqrt{1 - x^{2}}} + \frac{2 \operatorname{asin}{\left(x \right)}}{x^{3}}\right)
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5-я производная [src] 
  /                                                                       /         2          4   \                           \
  |                      /          2 \                                   |     30*x       35*x    |             /          2 \|
  |                      |       5*x  |                                 3*|3 - ------- + ----------|*log(x)      |       3*x  ||
  |                   15*|-3 + -------|                                   |          2            2|          10*|-1 + -------||
  |                      |           2|                                   |    -1 + x    /      2\ |             |           2||
  |        30            \     -1 + x /         20         24*asin(x)     \              \-1 + x / /             \     -1 + x /|
5*|- -------------- - ----------------- + -------------- + ---------- + ----------------------------------- + -----------------|
  |        ________              5/2                 3/2        5                           5/2                            3/2 |
  |   4   /      2       /     2\          2 /     2\          x                    /     2\                     2 /     2\    |
  \  x *\/  1 - x        \1 - x /         x *\1 - x /                               \1 - x /                    x *\1 - x /    /
5(−15(5x2x2−1−3)(1−x2)52+3(35x4(x2−1)2−30x2x2−1+3)log⁡(x)(1−x2)52+10(3x2x2−1−1)x2(1−x2)32+20x2(1−x2)32−30x41−x2+24asin⁡(x)x5)5 \left(- \frac{15 \left(\frac{5 x^{2}}{x^{2} - 1} - 3\right)}{\left(1 - x^{2}\right)^{\frac{5}{2}}} + \frac{3 \left(\frac{35 x^{4}}{\left(x^{2} - 1\right)^{2}} - \frac{30 x^{2}}{x^{2} - 1} + 3\right) \log{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} + \frac{10 \left(\frac{3 x^{2}}{x^{2} - 1} - 1\right)}{x^{2} \left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{20}{x^{2} \left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{30}{x^{4} \sqrt{1 - x^{2}}} + \frac{24 \operatorname{asin}{\left(x \right)}}{x^{5}}\right)
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Gráfico
Derivada de y=5ln*arcsinx
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