Sr Examen

Otras calculadoras


y=x*arcsin(3x)*(2-x^2)

Derivada de y=x*arcsin(3x)*(2-x^2)

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src]
            /     2\
x*asin(3*x)*\2 - x /
$$x \operatorname{asin}{\left(3 x \right)} \left(2 - x^{2}\right)$$
(x*asin(3*x))*(2 - x^2)
Gráfica
Primera derivada [src]
/     2\ /     3*x                 \      2          
\2 - x /*|------------- + asin(3*x)| - 2*x *asin(3*x)
         |   __________            |                 
         |  /        2             |                 
         \\/  1 - 9*x              /                 
$$- 2 x^{2} \operatorname{asin}{\left(3 x \right)} + \left(2 - x^{2}\right) \left(\frac{3 x}{\sqrt{1 - 9 x^{2}}} + \operatorname{asin}{\left(3 x \right)}\right)$$
Segunda derivada [src]
                                                                /           2  \
                                                      /      2\ |        9*x   |
                                                    3*\-2 + x /*|-2 + ---------|
                                                                |             2|
      /     3*x                 \                               \     -1 + 9*x /
- 4*x*|------------- + asin(3*x)| - 2*x*asin(3*x) + ----------------------------
      |   __________            |                             __________        
      |  /        2             |                            /        2         
      \\/  1 - 9*x              /                          \/  1 - 9*x          
$$- 4 x \left(\frac{3 x}{\sqrt{1 - 9 x^{2}}} + \operatorname{asin}{\left(3 x \right)}\right) - 2 x \operatorname{asin}{\left(3 x \right)} + \frac{3 \left(x^{2} - 2\right) \left(\frac{9 x^{2}}{9 x^{2} - 1} - 2\right)}{\sqrt{1 - 9 x^{2}}}$$
Tercera derivada [src]
  /                                   /           2  \       /           2  \          \
  |                                   |        9*x   |       |       27*x   | /      2\|
  |                               6*x*|-2 + ---------|   9*x*|-4 + ---------|*\-2 + x /|
  |                                   |             2|       |             2|          |
  |                    6*x            \     -1 + 9*x /       \     -1 + 9*x /          |
3*|-2*asin(3*x) - ------------- + -------------------- + ------------------------------|
  |                  __________         __________                         3/2         |
  |                 /        2         /        2                /       2\            |
  \               \/  1 - 9*x        \/  1 - 9*x                 \1 - 9*x /            /
$$3 \left(\frac{6 x \left(\frac{9 x^{2}}{9 x^{2} - 1} - 2\right)}{\sqrt{1 - 9 x^{2}}} - \frac{6 x}{\sqrt{1 - 9 x^{2}}} + \frac{9 x \left(x^{2} - 2\right) \left(\frac{27 x^{2}}{9 x^{2} - 1} - 4\right)}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}}} - 2 \operatorname{asin}{\left(3 x \right)}\right)$$
Gráfico
Derivada de y=x*arcsin(3x)*(2-x^2)