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y=(arcsin^4)*5x/3
Derivada de la función/ sin^4/ arcsin/ y=(arcsin^4)*5x/3

Derivada de y=(arcsin^4)*5x/3

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Solución

Ha introducido [src] 
    4       
asin (x)*5*x
------------
     3
x5asin⁡4(x)3\frac{x 5 \operatorname{asin}^{4}{\left(x \right)}}{3} 
((asin(x)^4*5)*x)/3
Gráfica
02468-8-6-4-2-1010-2525
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Primera derivada [src] 
      4               3   
5*asin (x)   20*x*asin (x)
---------- + -------------
    3             ________
                 /      2 
             3*\/  1 - x
20xasin⁡3(x)31−x2+5asin⁡4(x)3\frac{20 x \operatorname{asin}^{3}{\left(x \right)}}{3 \sqrt{1 - x^{2}}} + \frac{5 \operatorname{asin}^{4}{\left(x \right)}}{3}
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Segunda derivada [src] 
       2    /  /     3       x*asin(x) \    2*asin(x) \
20*asin (x)*|x*|- ------- + -----------| + -----------|
            |  |        2           3/2|      ________|
            |  |  -1 + x    /     2\   |     /      2 |
            \  \            \1 - x /   /   \/  1 - x  /
-------------------------------------------------------
                           3
20(x(xasin⁡(x)(1−x2)32−3x2−1)+2asin⁡(x)1−x2)asin⁡2(x)3\frac{20 \left(x \left(\frac{x \operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{3}{x^{2} - 1}\right) + \frac{2 \operatorname{asin}{\left(x \right)}}{\sqrt{1 - x^{2}}}\right) \operatorname{asin}^{2}{\left(x \right)}}{3}
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Tercera derivada [src] 
   /  /                    2          2     2                 \                                      \        
   |  |     6          asin (x)    3*x *asin (x)   9*x*asin(x)|     /     3       x*asin(x) \        |        
20*|x*|----------- + ----------- + ------------- + -----------| + 3*|- ------- + -----------|*asin(x)|*asin(x)
   |  |        3/2           3/2            5/2              2|     |        2           3/2|        |        
   |  |/     2\      /     2\       /     2\        /      2\ |     |  -1 + x    /     2\   |        |        
   \  \\1 - x /      \1 - x /       \1 - x /        \-1 + x / /     \            \1 - x /   /        /        
--------------------------------------------------------------------------------------------------------------
                                                      3
20(x(3x2asin⁡2(x)(1−x2)52+9xasin⁡(x)(x2−1)2+asin⁡2(x)(1−x2)32+6(1−x2)32)+3(xasin⁡(x)(1−x2)32−3x2−1)asin⁡(x))asin⁡(x)3\frac{20 \left(x \left(\frac{3 x^{2} \operatorname{asin}^{2}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} + \frac{9 x \operatorname{asin}{\left(x \right)}}{\left(x^{2} - 1\right)^{2}} + \frac{\operatorname{asin}^{2}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{6}{\left(1 - x^{2}\right)^{\frac{3}{2}}}\right) + 3 \left(\frac{x \operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{3}{x^{2} - 1}\right) \operatorname{asin}{\left(x \right)}\right) \operatorname{asin}{\left(x \right)}}{3}
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Gráfico
Derivada de y=(arcsin^4)*5x/3
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