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y=(arcsin(4x+x^3))^2
Derivada de la función/ x+x^3/ arcsin/ y=(arcsin(4x+x^3))^2

Derivada de y=(arcsin(4x+x^3))^2

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

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Solución

Ha introducido [src] 
    2/       3\
asin \4*x + x /
asin⁡2(x3+4x)\operatorname{asin}^{2}{\left(x^{3} + 4 x \right)} 
asin(4*x + x^3)^2
Gráfica
02468-8-6-4-2-1010-1010
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Primera derivada [src] 
  /       2\     /       3\
2*\4 + 3*x /*asin\4*x + x /
---------------------------
       _________________   
      /               2    
     /      /       3\     
   \/   1 - \4*x + x /
2(3x2+4)asin⁡(x3+4x)1−(x3+4x)2\frac{2 \left(3 x^{2} + 4\right) \operatorname{asin}{\left(x^{3} + 4 x \right)}}{\sqrt{1 - \left(x^{3} + 4 x\right)^{2}}}
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Segunda derivada [src] 
  /               2                                           2                          \
  |     /       2\                /  /     2\\      /       2\  /     2\     /  /     2\\|
  |     \4 + 3*x /        6*x*asin\x*\4 + x //    x*\4 + 3*x / *\4 + x /*asin\x*\4 + x //|
2*|- ----------------- + ---------------------- + ---------------------------------------|
  |                  2       __________________                              3/2         |
  |        2 /     2\       /                2             /               2\            |
  |  -1 + x *\4 + x /      /       2 /     2\              |     2 /     2\ |            |
  \                      \/   1 - x *\4 + x /              \1 - x *\4 + x / /            /
2(x(x2+4)(3x2+4)2asin⁡(x(x2+4))(−x2(x2+4)2+1)32+6xasin⁡(x(x2+4))−x2(x2+4)2+1−(3x2+4)2x2(x2+4)2−1)2 \left(\frac{x \left(x^{2} + 4\right) \left(3 x^{2} + 4\right)^{2} \operatorname{asin}{\left(x \left(x^{2} + 4\right) \right)}}{\left(- x^{2} \left(x^{2} + 4\right)^{2} + 1\right)^{\frac{3}{2}}} + \frac{6 x \operatorname{asin}{\left(x \left(x^{2} + 4\right) \right)}}{\sqrt{- x^{2} \left(x^{2} + 4\right)^{2} + 1}} - \frac{\left(3 x^{2} + 4\right)^{2}}{x^{2} \left(x^{2} + 4\right)^{2} - 1}\right)
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Tercera derivada [src] 
  /                                   3                                                      3                         2           3                                                              \
  |        /  /     2\\     /       2\      /  /     2\\         /       2\        /       2\  /     2\      2 /     2\  /       2\      /  /     2\\       2 /     2\ /       2\     /  /     2\\|
  |  6*asin\x*\4 + x //     \4 + 3*x / *asin\x*\4 + x //    18*x*\4 + 3*x /    3*x*\4 + 3*x / *\4 + x /   3*x *\4 + x / *\4 + 3*x / *asin\x*\4 + x //   18*x *\4 + x /*\4 + 3*x /*asin\x*\4 + x //|
2*|---------------------- + ---------------------------- - ----------------- + ------------------------ + ------------------------------------------- + ------------------------------------------|
  |    __________________                        3/2                       2                        2                                  5/2                                          3/2           |
  |   /                2       /               2\                2 /     2\      /                2\                 /               2\                           /               2\              |
  |  /       2 /     2\        |     2 /     2\ |          -1 + x *\4 + x /      |      2 /     2\ |                 |     2 /     2\ |                           |     2 /     2\ |              |
  \\/   1 - x *\4 + x /        \1 - x *\4 + x / /                                \-1 + x *\4 + x / /                 \1 - x *\4 + x / /                           \1 - x *\4 + x / /              /
2(3x2(x2+4)2(3x2+4)3asin⁡(x(x2+4))(−x2(x2+4)2+1)52+18x2(x2+4)(3x2+4)asin⁡(x(x2+4))(−x2(x2+4)2+1)32+3x(x2+4)(3x2+4)3(x2(x2+4)2−1)2−18x(3x2+4)x2(x2+4)2−1+(3x2+4)3asin⁡(x(x2+4))(−x2(x2+4)2+1)32+6asin⁡(x(x2+4))−x2(x2+4)2+1)2 \left(\frac{3 x^{2} \left(x^{2} + 4\right)^{2} \left(3 x^{2} + 4\right)^{3} \operatorname{asin}{\left(x \left(x^{2} + 4\right) \right)}}{\left(- x^{2} \left(x^{2} + 4\right)^{2} + 1\right)^{\frac{5}{2}}} + \frac{18 x^{2} \left(x^{2} + 4\right) \left(3 x^{2} + 4\right) \operatorname{asin}{\left(x \left(x^{2} + 4\right) \right)}}{\left(- x^{2} \left(x^{2} + 4\right)^{2} + 1\right)^{\frac{3}{2}}} + \frac{3 x \left(x^{2} + 4\right) \left(3 x^{2} + 4\right)^{3}}{\left(x^{2} \left(x^{2} + 4\right)^{2} - 1\right)^{2}} - \frac{18 x \left(3 x^{2} + 4\right)}{x^{2} \left(x^{2} + 4\right)^{2} - 1} + \frac{\left(3 x^{2} + 4\right)^{3} \operatorname{asin}{\left(x \left(x^{2} + 4\right) \right)}}{\left(- x^{2} \left(x^{2} + 4\right)^{2} + 1\right)^{\frac{3}{2}}} + \frac{6 \operatorname{asin}{\left(x \left(x^{2} + 4\right) \right)}}{\sqrt{- x^{2} \left(x^{2} + 4\right)^{2} + 1}}\right)
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Gráfico
Derivada de y=(arcsin(4x+x^3))^2
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