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arcsin(x)^sqrt(1-x^2)
Derivada de la función/ 1-x^2/ sin(x)/ arcsin/ arcsin(x)^sqrt(1-x^2)

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

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
            ________
           /      2 
         \/  1 - x  
(asin(x))
asin⁡1−x2(x)\operatorname{asin}^{\sqrt{1 - x^{2}}}{\left(x \right)} 
asin(x)^(sqrt(1 - x^2))
Solución detallada

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

    Perola derivada

    (1−x2)1−x22(log⁡(1−x2)+1)\left(1 - x^{2}\right)^{\frac{\sqrt{1 - x^{2}}}{2}} \left(\log{\left(\sqrt{1 - x^{2}} \right)} + 1\right)

  2. Simplificamos:

    (1−x2)1−x22(log⁡(1−x2)+2)2\frac{\left(1 - x^{2}\right)^{\frac{\sqrt{1 - x^{2}}}{2}} \left(\log{\left(1 - x^{2} \right)} + 2\right)}{2}

Respuesta:

(1−x2)1−x22(log⁡(1−x2)+2)2\frac{\left(1 - x^{2}\right)^{\frac{\sqrt{1 - x^{2}}}{2}} \left(\log{\left(1 - x^{2} \right)} + 2\right)}{2}

Gráfica
02468-8-6-4-2-101002
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Trazar el gráfico f'(x)
Primera derivada [src] 
            ________                           
           /      2                            
         \/  1 - x   /   1      x*log(asin(x))\
(asin(x))           *|------- - --------------|
                     |asin(x)       ________  |
                     |             /      2   |
                     \           \/  1 - x    /
(−xlog⁡(asin⁡(x))1−x2+1asin⁡(x))asin⁡1−x2(x)\left(- \frac{x \log{\left(\operatorname{asin}{\left(x \right)} \right)}}{\sqrt{1 - x^{2}}} + \frac{1}{\operatorname{asin}{\left(x \right)}}\right) \operatorname{asin}^{\sqrt{1 - x^{2}}}{\left(x \right)}
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Segunda derivada [src] 
            ________                                                                                                            
           /      2  /                            2                                                              2             \
         \/  1 - x   |/     1      x*log(asin(x))\             1             log(asin(x))           x           x *log(asin(x))|
(asin(x))           *||- ------- + --------------|  - -------------------- - ------------ + ----------------- - ---------------|
                     ||  asin(x)       ________  |       ________               ________    /      2\                     3/2  |
                     ||               /      2   |      /      2      2        /      2     \-1 + x /*asin(x)     /     2\     |
                     \\             \/  1 - x    /    \/  1 - x  *asin (x)   \/  1 - x                            \1 - x /     /
(−x2log⁡(asin⁡(x))(1−x2)32+x(x2−1)asin⁡(x)+(xlog⁡(asin⁡(x))1−x2−1asin⁡(x))2−log⁡(asin⁡(x))1−x2−11−x2asin⁡2(x))asin⁡1−x2(x)\left(- \frac{x^{2} \log{\left(\operatorname{asin}{\left(x \right)} \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{x}{\left(x^{2} - 1\right) \operatorname{asin}{\left(x \right)}} + \left(\frac{x \log{\left(\operatorname{asin}{\left(x \right)} \right)}}{\sqrt{1 - x^{2}}} - \frac{1}{\operatorname{asin}{\left(x \right)}}\right)^{2} - \frac{\log{\left(\operatorname{asin}{\left(x \right)} \right)}}{\sqrt{1 - x^{2}}} - \frac{1}{\sqrt{1 - x^{2}} \operatorname{asin}^{2}{\left(x \right)}}\right) \operatorname{asin}^{\sqrt{1 - x^{2}}}{\left(x \right)}
Simplificar
Tercera derivada [src] 
            ________                                                                                                                                                                                                                                                    
           /      2  /                              3                                                                           /                                       2                                 \                                2             3             \
         \/  1 - x   |  /     1      x*log(asin(x))\            2                    2             /     1      x*log(asin(x))\ |         1             log(asin(x))   x *log(asin(x))           x        |   3*x*log(asin(x))          3*x           3*x *log(asin(x))|
(asin(x))           *|- |- ------- + --------------|  - ------------------ + ----------------- + 3*|- ------- + --------------|*|-------------------- + ------------ + --------------- - -----------------| - ---------------- - ------------------ - -----------------|
                     |  |  asin(x)       ________  |    /      2\     3      /      2\             |  asin(x)       ________  | |   ________               ________              3/2     /      2\        |             3/2               2                      5/2   |
                     |  |               /      2   |    \-1 + x /*asin (x)   \-1 + x /*asin(x)     |               /      2   | |  /      2      2        /      2       /     2\        \-1 + x /*asin(x)|     /     2\         /      2\               /     2\      |
                     \  \             \/  1 - x    /                                               \             \/  1 - x    / \\/  1 - x  *asin (x)   \/  1 - x        \1 - x /                         /     \1 - x /         \-1 + x / *asin(x)      \1 - x /      /
(−3x3log⁡(asin⁡(x))(1−x2)52−3x2(x2−1)2asin⁡(x)−3xlog⁡(asin⁡(x))(1−x2)32−(xlog⁡(asin⁡(x))1−x2−1asin⁡(x))3+3(xlog⁡(asin⁡(x))1−x2−1asin⁡(x))(x2log⁡(asin⁡(x))(1−x2)32−x(x2−1)asin⁡(x)+log⁡(asin⁡(x))1−x2+11−x2asin⁡2(x))+2(x2−1)asin⁡(x)−2(x2−1)asin⁡3(x))asin⁡1−x2(x)\left(- \frac{3 x^{3} \log{\left(\operatorname{asin}{\left(x \right)} \right)}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} - \frac{3 x^{2}}{\left(x^{2} - 1\right)^{2} \operatorname{asin}{\left(x \right)}} - \frac{3 x \log{\left(\operatorname{asin}{\left(x \right)} \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \left(\frac{x \log{\left(\operatorname{asin}{\left(x \right)} \right)}}{\sqrt{1 - x^{2}}} - \frac{1}{\operatorname{asin}{\left(x \right)}}\right)^{3} + 3 \left(\frac{x \log{\left(\operatorname{asin}{\left(x \right)} \right)}}{\sqrt{1 - x^{2}}} - \frac{1}{\operatorname{asin}{\left(x \right)}}\right) \left(\frac{x^{2} \log{\left(\operatorname{asin}{\left(x \right)} \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{x}{\left(x^{2} - 1\right) \operatorname{asin}{\left(x \right)}} + \frac{\log{\left(\operatorname{asin}{\left(x \right)} \right)}}{\sqrt{1 - x^{2}}} + \frac{1}{\sqrt{1 - x^{2}} \operatorname{asin}^{2}{\left(x \right)}}\right) + \frac{2}{\left(x^{2} - 1\right) \operatorname{asin}{\left(x \right)}} - \frac{2}{\left(x^{2} - 1\right) \operatorname{asin}^{3}{\left(x \right)}}\right) \operatorname{asin}^{\sqrt{1 - x^{2}}}{\left(x \right)}
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Gráfico
Derivada de arcsin(x)^sqrt(1-x^2)
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