Производная (|x|)+1/(|x|)-3

Вы ввели

         1     
|x| + 1*--- - 3
        |x|    

$$\left|{x}\right| - 3 + 1 \cdot \frac{1}{\left|{x}\right|}$$

d /         1     \
--||x| + 1*--- - 3|
dx\        |x|    /

$$\frac{d}{d x} \left(\left|{x}\right| - 3 + 1 \cdot \frac{1}{\left|{x}\right|}\right)$$

Первая производная

  sign(x)          
- ------- + sign(x)
      2            
     x             

$$\operatorname{sign}{\left(x \right)} - \frac{\operatorname{sign}{\left(x \right)}}{x^{2}}$$

Вторая производная

  /sign(x)   DiracDelta(x)                \
2*|------- - ------------- + DiracDelta(x)|
  |    3            2                     |
  \   x            x                      /

$$2 \left(\delta\left(x\right) - \frac{\delta\left(x\right)}{x^{2}} + \frac{\operatorname{sign}{\left(x \right)}}{x^{3}}\right)$$

Третья производная

  /  DiracDelta(x, 1)   3*sign(x)   4*DiracDelta(x)                   \
2*|- ---------------- - --------- + --------------- + DiracDelta(x, 1)|
  |          2               4              3                         |
  \         x               x              x                          /

$$2 \left(\delta^{\left( 1 \right)}\left( x \right) - \frac{\delta^{\left( 1 \right)}\left( x \right)}{x^{2}} + \frac{4 \delta\left(x\right)}{x^{3}} - \frac{3 \operatorname{sign}{\left(x \right)}}{x^{4}}\right)$$

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