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Derivada de la función/ inx/x/ |x|sinx/x

Derivada de |x|sinx/x

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

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Solución

Ha introducido [src] 
|x|*sin(x)
----------
    x
sin⁡(x)∣x∣x\frac{\sin{\left(x \right)} \left|{x}\right|}{x} 
(|x|*sin(x))/x
Primera derivada [src] 
|x|*cos(x) + sign(x)*sin(x)   |x|*sin(x)
--------------------------- - ----------
             x                     2    
                                  x
sin⁡(x)sign⁡(x)+cos⁡(x)∣x∣x−sin⁡(x)∣x∣x2\frac{\sin{\left(x \right)} \operatorname{sign}{\left(x \right)} + \cos{\left(x \right)} \left|{x}\right|}{x} - \frac{\sin{\left(x \right)} \left|{x}\right|}{x^{2}}
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Segunda derivada [src] 
              2*(|x|*cos(x) + sign(x)*sin(x))                                               2*|x|*sin(x)
-|x|*sin(x) - ------------------------------- + 2*DiracDelta(x)*sin(x) + 2*cos(x)*sign(x) + ------------
                             x                                                                    2     
                                                                                                 x      
--------------------------------------------------------------------------------------------------------
                                                   x
−sin⁡(x)∣x∣+2sin⁡(x)δ(x)+2cos⁡(x)sign⁡(x)−2(sin⁡(x)sign⁡(x)+cos⁡(x)∣x∣)x+2sin⁡(x)∣x∣x2x\frac{- \sin{\left(x \right)} \left|{x}\right| + 2 \sin{\left(x \right)} \delta\left(x\right) + 2 \cos{\left(x \right)} \operatorname{sign}{\left(x \right)} - \frac{2 \left(\sin{\left(x \right)} \operatorname{sign}{\left(x \right)} + \cos{\left(x \right)} \left|{x}\right|\right)}{x} + \frac{2 \sin{\left(x \right)} \left|{x}\right|}{x^{2}}}{x}
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Tercera derivada [src] 
              3*(-|x|*sin(x) + 2*DiracDelta(x)*sin(x) + 2*cos(x)*sign(x))                                                  6*(|x|*cos(x) + sign(x)*sin(x))                            6*|x|*sin(x)
-|x|*cos(x) - ----------------------------------------------------------- - 3*sign(x)*sin(x) + 2*DiracDelta(x, 1)*sin(x) + ------------------------------- + 6*DiracDelta(x)*cos(x) - ------------
                                           x                                                                                               2                                                3     
                                                                                                                                          x                                                x      
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                x
2sin⁡(x)δ(1)(x)−3sin⁡(x)sign⁡(x)−cos⁡(x)∣x∣+6cos⁡(x)δ(x)−3(−sin⁡(x)∣x∣+2sin⁡(x)δ(x)+2cos⁡(x)sign⁡(x))x+6(sin⁡(x)sign⁡(x)+cos⁡(x)∣x∣)x2−6sin⁡(x)∣x∣x3x\frac{2 \sin{\left(x \right)} \delta^{\left( 1 \right)}\left( x \right) - 3 \sin{\left(x \right)} \operatorname{sign}{\left(x \right)} - \cos{\left(x \right)} \left|{x}\right| + 6 \cos{\left(x \right)} \delta\left(x\right) - \frac{3 \left(- \sin{\left(x \right)} \left|{x}\right| + 2 \sin{\left(x \right)} \delta\left(x\right) + 2 \cos{\left(x \right)} \operatorname{sign}{\left(x \right)}\right)}{x} + \frac{6 \left(\sin{\left(x \right)} \operatorname{sign}{\left(x \right)} + \cos{\left(x \right)} \left|{x}\right|\right)}{x^{2}} - \frac{6 \sin{\left(x \right)} \left|{x}\right|}{x^{3}}}{x}
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