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Derivada de la función/ abs(x)/ -((x)*sin(sqrt(abs(x))))

Derivada de -((x)*sin(sqrt(abs(x))))

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

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Solución

Ha introducido [src] 
      /  _____\
-x*sin\\/ |x| /
−xsin⁡(∣x∣)- x \sin{\left(\sqrt{\left|{x}\right|} \right)} 
-x*sin(sqrt(|x|))
Primera derivada [src] 
                      /  _____\        
     /  _____\   x*cos\\/ |x| /*sign(x)
- sin\\/ |x| / - ----------------------
                           _____       
                       2*\/ |x|
−xcos⁡(∣x∣)sign⁡(x)2∣x∣−sin⁡(∣x∣)- \frac{x \cos{\left(\sqrt{\left|{x}\right|} \right)} \operatorname{sign}{\left(x \right)}}{2 \sqrt{\left|{x}\right|}} - \sin{\left(\sqrt{\left|{x}\right|} \right)}
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Segunda derivada [src] 
  /    2       /  _____\       2       /  _____\                      /  _____\\                       
  |sign (x)*sin\\/ |x| /   sign (x)*cos\\/ |x| /   4*DiracDelta(x)*cos\\/ |x| /|                       
x*|--------------------- + --------------------- - ----------------------------|                       
  |         |x|                       3/2                      _____           |      /  _____\        
  \                                |x|                       \/ |x|            /   cos\\/ |x| /*sign(x)
-------------------------------------------------------------------------------- - --------------------
                                       4                                                   _____       
                                                                                         \/ |x|
x(sin⁡(∣x∣)sign⁡2(x)∣x∣−4cos⁡(∣x∣)δ(x)∣x∣+cos⁡(∣x∣)sign⁡2(x)∣x∣32)4−cos⁡(∣x∣)sign⁡(x)∣x∣\frac{x \left(\frac{\sin{\left(\sqrt{\left|{x}\right|} \right)} \operatorname{sign}^{2}{\left(x \right)}}{\left|{x}\right|} - \frac{4 \cos{\left(\sqrt{\left|{x}\right|} \right)} \delta\left(x\right)}{\sqrt{\left|{x}\right|}} + \frac{\cos{\left(\sqrt{\left|{x}\right|} \right)} \operatorname{sign}^{2}{\left(x \right)}}{\left|{x}\right|^{\frac{3}{2}}}\right)}{4} - \frac{\cos{\left(\sqrt{\left|{x}\right|} \right)} \operatorname{sign}{\left(x \right)}}{\sqrt{\left|{x}\right|}}
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Tercera derivada [src] 
  /    3       /  _____\                         /  _____\         3       /  _____\         3       /  _____\                               /  _____\                       /  _____\        \                                                                                   
  |sign (x)*cos\\/ |x| /   8*DiracDelta(x, 1)*cos\\/ |x| /   3*sign (x)*sin\\/ |x| /   3*sign (x)*cos\\/ |x| /   12*DiracDelta(x)*sign(x)*sin\\/ |x| /   12*DiracDelta(x)*cos\\/ |x| /*sign(x)|                                                                                   
x*|--------------------- - ------------------------------- - ----------------------- - ----------------------- + ------------------------------------- + -------------------------------------|                                                                                   
  |           3/2                        _____                           2                         5/2                            |x|                                       3/2               |                      /  _____\         2       /  _____\         2       /  _____\
  \        |x|                         \/ |x|                           x                       |x|                                                                      |x|                  /   3*DiracDelta(x)*cos\\/ |x| /   3*sign (x)*sin\\/ |x| /   3*sign (x)*cos\\/ |x| /
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ---------------------------- + ----------------------- + -----------------------
                                                                                               8                                                                                                              _____                       4*|x|                         3/2       
                                                                                                                                                                                                            \/ |x|                                                 4*|x|
x(12sin⁡(∣x∣)δ(x)sign⁡(x)∣x∣−8cos⁡(∣x∣)δ(1)(x)∣x∣+12cos⁡(∣x∣)δ(x)sign⁡(x)∣x∣32+cos⁡(∣x∣)sign⁡3(x)∣x∣32−3cos⁡(∣x∣)sign⁡3(x)∣x∣52−3sin⁡(∣x∣)sign⁡3(x)x2)8+3sin⁡(∣x∣)sign⁡2(x)4∣x∣−3cos⁡(∣x∣)δ(x)∣x∣+3cos⁡(∣x∣)sign⁡2(x)4∣x∣32\frac{x \left(\frac{12 \sin{\left(\sqrt{\left|{x}\right|} \right)} \delta\left(x\right) \operatorname{sign}{\left(x \right)}}{\left|{x}\right|} - \frac{8 \cos{\left(\sqrt{\left|{x}\right|} \right)} \delta^{\left( 1 \right)}\left( x \right)}{\sqrt{\left|{x}\right|}} + \frac{12 \cos{\left(\sqrt{\left|{x}\right|} \right)} \delta\left(x\right) \operatorname{sign}{\left(x \right)}}{\left|{x}\right|^{\frac{3}{2}}} + \frac{\cos{\left(\sqrt{\left|{x}\right|} \right)} \operatorname{sign}^{3}{\left(x \right)}}{\left|{x}\right|^{\frac{3}{2}}} - \frac{3 \cos{\left(\sqrt{\left|{x}\right|} \right)} \operatorname{sign}^{3}{\left(x \right)}}{\left|{x}\right|^{\frac{5}{2}}} - \frac{3 \sin{\left(\sqrt{\left|{x}\right|} \right)} \operatorname{sign}^{3}{\left(x \right)}}{x^{2}}\right)}{8} + \frac{3 \sin{\left(\sqrt{\left|{x}\right|} \right)} \operatorname{sign}^{2}{\left(x \right)}}{4 \left|{x}\right|} - \frac{3 \cos{\left(\sqrt{\left|{x}\right|} \right)} \delta\left(x\right)}{\sqrt{\left|{x}\right|}} + \frac{3 \cos{\left(\sqrt{\left|{x}\right|} \right)} \operatorname{sign}^{2}{\left(x \right)}}{4 \left|{x}\right|^{\frac{3}{2}}}
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