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y=x^5arcsin2x
Derivada de la función/ sin2x/ y=x^5/ arcsin/ y=x^5arcsin2x

Derivada de y=x^5arcsin2x

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

Ha introducido [src] 
 5          
x *asin(2*x)
$$x^{5} \operatorname{asin}{\left(2 x \right)}$$ 
x^5*asin(2*x)
Gráfica
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
        5                     
     2*x           4          
------------- + 5*x *asin(2*x)
   __________                 
  /        2                  
\/  1 - 4*x
$$\frac{2 x^{5}}{\sqrt{1 - 4 x^{2}}} + 5 x^{4} \operatorname{asin}{\left(2 x \right)}$$
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Segunda derivada [src] 
     /                      3                    \
   3 |                   2*x             5*x     |
4*x *|5*asin(2*x) + ------------- + -------------|
     |                        3/2      __________|
     |              /       2\        /        2 |
     \              \1 - 4*x /      \/  1 - 4*x  /
$$4 x^{3} \left(\frac{2 x^{3}}{\left(1 - 4 x^{2}\right)^{\frac{3}{2}}} + \frac{5 x}{\sqrt{1 - 4 x^{2}}} + 5 \operatorname{asin}{\left(2 x \right)}\right)$$
Simplificar
3-я производная [src] 
     /                                                    /           2  \\
     |                                                  3 |       12*x   ||
     |                                               2*x *|-1 + ---------||
     |                                       3            |             2||
   2 |                    30*x           30*x             \     -1 + 4*x /|
4*x *|15*asin(2*x) + ------------- + ------------- - ---------------------|
     |                  __________             3/2                 3/2    |
     |                 /        2    /       2\          /       2\       |
     \               \/  1 - 4*x     \1 - 4*x /          \1 - 4*x /       /
$$4 x^{2} \left(- \frac{2 x^{3} \left(\frac{12 x^{2}}{4 x^{2} - 1} - 1\right)}{\left(1 - 4 x^{2}\right)^{\frac{3}{2}}} + \frac{30 x^{3}}{\left(1 - 4 x^{2}\right)^{\frac{3}{2}}} + \frac{30 x}{\sqrt{1 - 4 x^{2}}} + 15 \operatorname{asin}{\left(2 x \right)}\right)$$
Simplificar
Tercera derivada [src] 
     /                                                    /           2  \\
     |                                                  3 |       12*x   ||
     |                                               2*x *|-1 + ---------||
     |                                       3            |             2||
   2 |                    30*x           30*x             \     -1 + 4*x /|
4*x *|15*asin(2*x) + ------------- + ------------- - ---------------------|
     |                  __________             3/2                 3/2    |
     |                 /        2    /       2\          /       2\       |
     \               \/  1 - 4*x     \1 - 4*x /          \1 - 4*x /       /
$$4 x^{2} \left(- \frac{2 x^{3} \left(\frac{12 x^{2}}{4 x^{2} - 1} - 1\right)}{\left(1 - 4 x^{2}\right)^{\frac{3}{2}}} + \frac{30 x^{3}}{\left(1 - 4 x^{2}\right)^{\frac{3}{2}}} + \frac{30 x}{\sqrt{1 - 4 x^{2}}} + 15 \operatorname{asin}{\left(2 x \right)}\right)$$
Simplificar
Gráfico
Derivada de y=x^5arcsin2x
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