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y=arcsinx^(1/5)
Derivada de la función/ arcsin/ x^(1/5)/ y=arcsinx^(1/5)

Derivada de y=arcsinx^(1/5)

Función f() - derivada -er orden en el punto
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Gráfico:

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Solución

Ha introducido [src] 
5 _________
\/ asin(x)
asin⁡(x)5\sqrt[5]{\operatorname{asin}{\left(x \right)}} 
asin(x)^(1/5)
Gráfica
02468-8-6-4-2-101002
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Trazar el gráfico f'(x)
Primera derivada [src] 
           1            
------------------------
     ________           
    /      2      4/5   
5*\/  1 - x  *asin   (x)
151−x2asin⁡45(x)\frac{1}{5 \sqrt{1 - x^{2}} \operatorname{asin}^{\frac{4}{5}}{\left(x \right)}}
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Segunda derivada [src] 
        4               5*x    
----------------- + -----------
/      2\                   3/2
\-1 + x /*asin(x)   /     2\   
                    \1 - x /   
-------------------------------
                4/5            
         25*asin   (x)
5x(1−x2)32+4(x2−1)asin⁡(x)25asin⁡45(x)\frac{\frac{5 x}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{4}{\left(x^{2} - 1\right) \operatorname{asin}{\left(x \right)}}}{25 \operatorname{asin}^{\frac{4}{5}}{\left(x \right)}}
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Tercera derivada [src] 
                                            2                        
     25                36               75*x              60*x       
----------- + -------------------- + ----------- - ------------------
        3/2           3/2                    5/2            2        
/     2\      /     2\        2      /     2\      /      2\         
\1 - x /      \1 - x /   *asin (x)   \1 - x /      \-1 + x / *asin(x)
---------------------------------------------------------------------
                                    4/5                              
                            125*asin   (x)
75x2(1−x2)52−60x(x2−1)2asin⁡(x)+25(1−x2)32+36(1−x2)32asin⁡2(x)125asin⁡45(x)\frac{\frac{75 x^{2}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} - \frac{60 x}{\left(x^{2} - 1\right)^{2} \operatorname{asin}{\left(x \right)}} + \frac{25}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{36}{\left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{asin}^{2}{\left(x \right)}}}{125 \operatorname{asin}^{\frac{4}{5}}{\left(x \right)}}
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Gráfico
Derivada de y=arcsinx^(1/5)
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