Sr Examen

Derivada de xsinc

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src]
x*sinc(x)
$$x \operatorname{sinc}{\left(x \right)}$$
x*sinc(x)
Gráfica
Primera derivada [src]
  //-sin(x) + x*cos(x)            \          
  ||------------------  for x != 0|          
  ||         2                    |          
x*|<        x                     | + sinc(x)
  ||                              |          
  ||        0           otherwise |          
  \\                              /          
$$x \left(\begin{cases} \frac{x \cos{\left(x \right)} - \sin{\left(x \right)}}{x^{2}} & \text{for}\: x \neq 0 \\0 & \text{otherwise} \end{cases}\right) + \operatorname{sinc}{\left(x \right)}$$
Segunda derivada [src]
                                        // /2*(-sin(x) + x*cos(x))         \             \
  //-sin(x) + x*cos(x)            \     ||-|---------------------- + sin(x)|             |
  ||------------------  for x != 0|     || |           2                   |             |
  ||         2                    |     || \          x                    /             |
2*|<        x                     | + x*|<-----------------------------------  for x != 0|
  ||                              |     ||                 x                             |
  ||        0           otherwise |     ||                                               |
  \\                              /     ||                 0                   otherwise |
                                        \\                                               /
$$x \left(\begin{cases} - \frac{\sin{\left(x \right)} + \frac{2 \left(x \cos{\left(x \right)} - \sin{\left(x \right)}\right)}{x^{2}}}{x} & \text{for}\: x \neq 0 \\0 & \text{otherwise} \end{cases}\right) + 2 \left(\begin{cases} \frac{x \cos{\left(x \right)} - \sin{\left(x \right)}}{x^{2}} & \text{for}\: x \neq 0 \\0 & \text{otherwise} \end{cases}\right)$$
Tercera derivada [src]
  // /2*(-sin(x) + x*cos(x))         \             \     //          3*sin(x)   6*(-sin(x) + x*cos(x))            \
  ||-|---------------------- + sin(x)|             |     ||-cos(x) + -------- + ----------------------            |
  || |           2                   |             |     ||             x                  3                      |
  || \          x                    /             |     ||                               x                       |
3*|<-----------------------------------  for x != 0| + x*|<-------------------------------------------  for x != 0|
  ||                 x                             |     ||                     x                                 |
  ||                                               |     ||                                                       |
  ||                 0                   otherwise |     ||                     0                       otherwise |
  \\                                               /     \\                                                       /
$$x \left(\begin{cases} \frac{- \cos{\left(x \right)} + \frac{3 \sin{\left(x \right)}}{x} + \frac{6 \left(x \cos{\left(x \right)} - \sin{\left(x \right)}\right)}{x^{3}}}{x} & \text{for}\: x \neq 0 \\0 & \text{otherwise} \end{cases}\right) + 3 \left(\begin{cases} - \frac{\sin{\left(x \right)} + \frac{2 \left(x \cos{\left(x \right)} - \sin{\left(x \right)}\right)}{x^{2}}}{x} & \text{for}\: x \neq 0 \\0 & \text{otherwise} \end{cases}\right)$$
Gráfico
Derivada de xsinc