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y=x^arcsin^2x
Derivada de la función/ sin^2/ y=x^a/ arcsin/ y=x^arcsin^2x

Derivada de y=x^arcsin^2x

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

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Solución

Ha introducido [src] 
     2   
 asin (x)
x
xasin⁡2(x)x^{\operatorname{asin}^{2}{\left(x \right)}} 
x^(asin(x)^2)
Solución detallada

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

    Perola derivada

    (log⁡(asin⁡2(x))+1)(asin⁡2(x))asin⁡2(x)\left(\log{\left(\operatorname{asin}^{2}{\left(x \right)} \right)} + 1\right) \left(\operatorname{asin}^{2}{\left(x \right)}\right)^{\operatorname{asin}^{2}{\left(x \right)}}

Respuesta:

(log⁡(asin⁡2(x))+1)(asin⁡2(x))asin⁡2(x)\left(\log{\left(\operatorname{asin}^{2}{\left(x \right)} \right)} + 1\right) \left(\operatorname{asin}^{2}{\left(x \right)}\right)^{\operatorname{asin}^{2}{\left(x \right)}}

Gráfica
02468-8-6-4-2-10102-2
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
     2    /    2                      \
 asin (x) |asin (x)   2*asin(x)*log(x)|
x        *|-------- + ----------------|
          |   x            ________   |
          |               /      2    |
          \             \/  1 - x     /
xasin⁡2(x)(2log⁡(x)asin⁡(x)1−x2+asin⁡2(x)x)x^{\operatorname{asin}^{2}{\left(x \right)}} \left(\frac{2 \log{\left(x \right)} \operatorname{asin}{\left(x \right)}}{\sqrt{1 - x^{2}}} + \frac{\operatorname{asin}^{2}{\left(x \right)}}{x}\right)
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Segunda derivada [src] 
     2    /                       2                2                                                   \
 asin (x) |/asin(x)     2*log(x) \      2      asin (x)   2*log(x)     4*asin(x)     2*x*asin(x)*log(x)|
x        *||------- + -----------| *asin (x) - -------- - -------- + ------------- + ------------------|
          ||   x         ________|                 2            2         ________              3/2    |
          ||            /      2 |                x       -1 + x         /      2       /     2\       |
          \\          \/  1 - x  /                                   x*\/  1 - x        \1 - x /       /
xasin⁡2(x)(2xlog⁡(x)asin⁡(x)(1−x2)32+(2log⁡(x)1−x2+asin⁡(x)x)2asin⁡2(x)−2log⁡(x)x2−1+4asin⁡(x)x1−x2−asin⁡2(x)x2)x^{\operatorname{asin}^{2}{\left(x \right)}} \left(\frac{2 x \log{\left(x \right)} \operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \left(\frac{2 \log{\left(x \right)}}{\sqrt{1 - x^{2}}} + \frac{\operatorname{asin}{\left(x \right)}}{x}\right)^{2} \operatorname{asin}^{2}{\left(x \right)} - \frac{2 \log{\left(x \right)}}{x^{2} - 1} + \frac{4 \operatorname{asin}{\left(x \right)}}{x \sqrt{1 - x^{2}}} - \frac{\operatorname{asin}^{2}{\left(x \right)}}{x^{2}}\right)
Simplificar
Tercera derivada [src] 
     2    /                       3                                2                                                                                  /      2                                                   \                           2               \
 asin (x) |/asin(x)     2*log(x) \      3           6        2*asin (x)    6*asin(x)      6*asin(x)      2*asin(x)*log(x)     /asin(x)     2*log(x) \ |  asin (x)   2*log(x)     4*asin(x)     2*x*asin(x)*log(x)|           6*x*log(x)   6*x *asin(x)*log(x)|
x        *||------- + -----------| *asin (x) - ----------- + ---------- + ----------- - -------------- + ---------------- + 3*|------- + -----------|*|- -------- - -------- + ------------- + ------------------|*asin(x) + ---------- + -------------------|
          ||   x         ________|               /      2\        3               3/2         ________             3/2        |   x         ________| |      2            2         ________              3/2    |                    2               5/2    |
          ||            /      2 |             x*\-1 + x /       x        /     2\       2   /      2      /     2\           |            /      2 | |     x       -1 + x         /      2       /     2\       |           /      2\        /     2\       |
          \\          \/  1 - x  /                                        \1 - x /      x *\/  1 - x       \1 - x /           \          \/  1 - x  / \                        x*\/  1 - x        \1 - x /       /           \-1 + x /        \1 - x /       /
xasin⁡2(x)(6x2log⁡(x)asin⁡(x)(1−x2)52+6xlog⁡(x)(x2−1)2+(2log⁡(x)1−x2+asin⁡(x)x)3asin⁡3(x)+3(2log⁡(x)1−x2+asin⁡(x)x)(2xlog⁡(x)asin⁡(x)(1−x2)32−2log⁡(x)x2−1+4asin⁡(x)x1−x2−asin⁡2(x)x2)asin⁡(x)+2log⁡(x)asin⁡(x)(1−x2)32+6asin⁡(x)(1−x2)32−6x(x2−1)−6asin⁡(x)x21−x2+2asin⁡2(x)x3)x^{\operatorname{asin}^{2}{\left(x \right)}} \left(\frac{6 x^{2} \log{\left(x \right)} \operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} + \frac{6 x \log{\left(x \right)}}{\left(x^{2} - 1\right)^{2}} + \left(\frac{2 \log{\left(x \right)}}{\sqrt{1 - x^{2}}} + \frac{\operatorname{asin}{\left(x \right)}}{x}\right)^{3} \operatorname{asin}^{3}{\left(x \right)} + 3 \left(\frac{2 \log{\left(x \right)}}{\sqrt{1 - x^{2}}} + \frac{\operatorname{asin}{\left(x \right)}}{x}\right) \left(\frac{2 x \log{\left(x \right)} \operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{2 \log{\left(x \right)}}{x^{2} - 1} + \frac{4 \operatorname{asin}{\left(x \right)}}{x \sqrt{1 - x^{2}}} - \frac{\operatorname{asin}^{2}{\left(x \right)}}{x^{2}}\right) \operatorname{asin}{\left(x \right)} + \frac{2 \log{\left(x \right)} \operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{6 \operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{6}{x \left(x^{2} - 1\right)} - \frac{6 \operatorname{asin}{\left(x \right)}}{x^{2} \sqrt{1 - x^{2}}} + \frac{2 \operatorname{asin}^{2}{\left(x \right)}}{x^{3}}\right)
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Gráfico
Derivada de y=x^arcsin^2x
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