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y=x^4*sin^3(5x)-arcsin3x

Derivada de y=x^4*sin^3(5x)-arcsin3x

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

Ha introducido [src]
 4    3                 
x *sin (5*x) - asin(3*x)
$$x^{4} \sin^{3}{\left(5 x \right)} - \operatorname{asin}{\left(3 x \right)}$$
x^4*sin(5*x)^3 - asin(3*x)
Gráfica
Primera derivada [src]
        3            3    3            4    2              
- ------------- + 4*x *sin (5*x) + 15*x *sin (5*x)*cos(5*x)
     __________                                            
    /        2                                             
  \/  1 - 9*x                                              
$$15 x^{4} \sin^{2}{\left(5 x \right)} \cos{\left(5 x \right)} + 4 x^{3} \sin^{3}{\left(5 x \right)} - \frac{3}{\sqrt{1 - 9 x^{2}}}$$
Segunda derivada [src]
    /        9             3    3               3            2    2                     3    2              \
3*x*|- ------------- - 25*x *sin (5*x) + 4*x*sin (5*x) + 40*x *sin (5*x)*cos(5*x) + 50*x *cos (5*x)*sin(5*x)|
    |            3/2                                                                                        |
    |  /       2\                                                                                           |
    \  \1 - 9*x /                                                                                           /
$$3 x \left(- 25 x^{3} \sin^{3}{\left(5 x \right)} + 50 x^{3} \sin{\left(5 x \right)} \cos^{2}{\left(5 x \right)} + 40 x^{2} \sin^{2}{\left(5 x \right)} \cos{\left(5 x \right)} + 4 x \sin^{3}{\left(5 x \right)} - \frac{9}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}}}\right)$$
Tercera derivada [src]
  /                                              2                                                                                                                          \
  |        9              3    3            243*x              3             4    3             4    2                      2    2                      3    2              |
3*|- ------------- - 300*x *sin (5*x) - ------------- + 8*x*sin (5*x) + 250*x *cos (5*x) - 875*x *sin (5*x)*cos(5*x) + 180*x *sin (5*x)*cos(5*x) + 600*x *cos (5*x)*sin(5*x)|
  |            3/2                                5/2                                                                                                                       |
  |  /       2\                         /       2\                                                                                                                          |
  \  \1 - 9*x /                         \1 - 9*x /                                                                                                                          /
$$3 \left(- 875 x^{4} \sin^{2}{\left(5 x \right)} \cos{\left(5 x \right)} + 250 x^{4} \cos^{3}{\left(5 x \right)} - 300 x^{3} \sin^{3}{\left(5 x \right)} + 600 x^{3} \sin{\left(5 x \right)} \cos^{2}{\left(5 x \right)} + 180 x^{2} \sin^{2}{\left(5 x \right)} \cos{\left(5 x \right)} - \frac{243 x^{2}}{\left(1 - 9 x^{2}\right)^{\frac{5}{2}}} + 8 x \sin^{3}{\left(5 x \right)} - \frac{9}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}}}\right)$$
Gráfico
Derivada de y=x^4*sin^3(5x)-arcsin3x