Производная sin(|x|)

Вы ввели

sin(|x|)

$$\sin{\left(\left|{x}\right| \right)}$$

d           
--(sin(|x|))
dx          

$$\frac{d}{d x} \sin{\left(\left|{x}\right| \right)}$$

Первая производная

cos(|x|)*sign(x)

$$\cos{\left(\left|{x}\right| \right)} \operatorname{sign}{\left(x \right)}$$

Вторая производная

      2                                       
- sign (x)*sin(|x|) + 2*DiracDelta(x)*cos(|x|)

$$- \sin{\left(\left|{x}\right| \right)} \operatorname{sign}^{2}{\left(x \right)} + 2 \cos{\left(\left|{x}\right| \right)} \delta\left(x\right)$$

Третья производная

      3                                                                             
- sign (x)*cos(|x|) + 2*DiracDelta(x, 1)*cos(|x|) - 6*DiracDelta(x)*sign(x)*sin(|x|)

$$- 6 \sin{\left(\left|{x}\right| \right)} \delta\left(x\right) \operatorname{sign}{\left(x \right)} + 2 \cos{\left(\left|{x}\right| \right)} \delta^{\left( 1 \right)}\left( x \right) - \cos{\left(\left|{x}\right| \right)} \operatorname{sign}^{3}{\left(x \right)}$$

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