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x^3*arcsin(sqrt(1-x^2))+9/x^3
Derivada de la función/ arcsin(sqrt(1-x^2))/ x^3*arcsin(sqrt(1-x^2))+9/x^3

Derivada de x^3*arcsin(sqrt(1-x^2))+9/x^3

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

Ha introducido [src] 
       /   ________\     
 3     |  /      2 |   9 
x *asin\\/  1 - x  / + --
                        3
                       x
x3asin⁡(1−x2)+9x3x^{3} \operatorname{asin}{\left(\sqrt{1 - x^{2}} \right)} + \frac{9}{x^{3}} 
x^3*asin(sqrt(1 - x^2)) + 9/x^3
Gráfica
02468-8-6-4-2-1010-500000250000
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
                /   ________\           4      
  27      2     |  /      2 |          x       
- -- + 3*x *asin\\/  1 - x  / - ---------------
   4                               ________    
  x                               /      2     
                                \/  1 - x  *|x|
−x41−x2∣x∣+3x2asin⁡(1−x2)−27x4- \frac{x^{4}}{\sqrt{1 - x^{2}} \left|{x}\right|} + 3 x^{2} \operatorname{asin}{\left(\sqrt{1 - x^{2}} \right)} - \frac{27}{x^{4}}
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Segunda derivada [src] 
              /   ________\     2                   5                  3     
108           |  /      2 |    x *sign(x)          x                7*x      
--- + 6*x*asin\\/  1 - x  / + ----------- - --------------- - ---------------
  5                              ________           3/2          ________    
 x                              /      2    /     2\            /      2     
                              \/  1 - x     \1 - x /   *|x|   \/  1 - x  *|x|
−x5(1−x2)32∣x∣−7x31−x2∣x∣+x2sign⁡(x)1−x2+6xasin⁡(1−x2)+108x5- \frac{x^{5}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \left|{x}\right|} - \frac{7 x^{3}}{\sqrt{1 - x^{2}} \left|{x}\right|} + \frac{x^{2} \operatorname{sign}{\left(x \right)}}{\sqrt{1 - x^{2}}} + 6 x \operatorname{asin}{\left(\sqrt{1 - x^{2}} \right)} + \frac{108}{x^{5}}
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Tercera derivada [src] 
              /   ________\            2                 4                 6           2                    3                      
  540         |  /      2 |        27*x              12*x               3*x         2*x *DiracDelta(x)   2*x *sign(x)   9*x*sign(x)
- --- + 6*asin\\/  1 - x  / - --------------- - --------------- - --------------- + ------------------ + ------------ + -----------
    6                            ________               3/2               5/2             ________               3/2       ________
   x                            /      2        /     2\          /     2\               /      2        /     2\         /      2 
                              \/  1 - x  *|x|   \1 - x /   *|x|   \1 - x /   *|x|      \/  1 - x         \1 - x /       \/  1 - x
−3x6(1−x2)52∣x∣−12x4(1−x2)32∣x∣+2x3sign⁡(x)(1−x2)32+2x2δ(x)1−x2−27x21−x2∣x∣+9xsign⁡(x)1−x2+6asin⁡(1−x2)−540x6- \frac{3 x^{6}}{\left(1 - x^{2}\right)^{\frac{5}{2}} \left|{x}\right|} - \frac{12 x^{4}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \left|{x}\right|} + \frac{2 x^{3} \operatorname{sign}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{2 x^{2} \delta\left(x\right)}{\sqrt{1 - x^{2}}} - \frac{27 x^{2}}{\sqrt{1 - x^{2}} \left|{x}\right|} + \frac{9 x \operatorname{sign}{\left(x \right)}}{\sqrt{1 - x^{2}}} + 6 \operatorname{asin}{\left(\sqrt{1 - x^{2}} \right)} - \frac{540}{x^{6}}
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Gráfico
Derivada de x^3*arcsin(sqrt(1-x^2))+9/x^3
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