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Derivada de la función/ cos(x)/ sin(x)/ |x|/sin(x)*cos(x)

Derivada de |x|/sin(x)*cos(x)

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

Ha introducido [src] 
 |x|         
------*cos(x)
sin(x)
∣x∣sin⁡(x)cos⁡(x)\frac{\left|{x}\right|}{\sin{\left(x \right)}} \cos{\left(x \right)} 
(|x|/sin(x))*cos(x)
Primera derivada [src] 
       /sign(x)   |x|*cos(x)\       
-|x| + |------- - ----------|*cos(x)
       | sin(x)       2     |       
       \           sin (x)  /
(sign⁡(x)sin⁡(x)−cos⁡(x)∣x∣sin⁡2(x))cos⁡(x)−∣x∣\left(\frac{\operatorname{sign}{\left(x \right)}}{\sin{\left(x \right)}} - \frac{\cos{\left(x \right)} \left|{x}\right|}{\sin^{2}{\left(x \right)}}\right) \cos{\left(x \right)} - \left|{x}\right|
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Segunda derivada [src] 
             /                  /         2   \                       \                    
             |                  |    2*cos (x)|       2*cos(x)*sign(x)|                    
             |2*DiracDelta(x) + |1 + ---------|*|x| - ----------------|*cos(x)             
             |                  |        2    |            sin(x)     |                    
             \                  \     sin (x) /                       /          |x|*cos(x)
-2*sign(x) + ----------------------------------------------------------------- + ----------
                                           sin(x)                                  sin(x)
((1+2cos⁡2(x)sin⁡2(x))∣x∣+2δ(x)−2cos⁡(x)sign⁡(x)sin⁡(x))cos⁡(x)sin⁡(x)−2sign⁡(x)+cos⁡(x)∣x∣sin⁡(x)\frac{\left(\left(1 + \frac{2 \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) \left|{x}\right| + 2 \delta\left(x\right) - \frac{2 \cos{\left(x \right)} \operatorname{sign}{\left(x \right)}}{\sin{\left(x \right)}}\right) \cos{\left(x \right)}}{\sin{\left(x \right)}} - 2 \operatorname{sign}{\left(x \right)} + \frac{\cos{\left(x \right)} \left|{x}\right|}{\sin{\left(x \right)}}
Simplificar
Tercera derivada [src] 
                                           /                                                                          /         2   \           \                                                                    
                                           |                                                                          |    6*cos (x)|           |                                                                    
                                           |                                                                          |5 + ---------|*|x|*cos(x)|                                                                    
                                           |                       /         2   \                                    |        2    |           |                                                                    
                                           |                       |    2*cos (x)|           6*DiracDelta(x)*cos(x)   \     sin (x) /           |                                                                    
                                           |2*DiracDelta(x, 1) + 3*|1 + ---------|*sign(x) - ---------------------- - --------------------------|*cos(x)     /  |x|*cos(x)          \                                
                     /         2   \       |                       |        2    |                   sin(x)                     sin(x)          |          3*|- ---------- + sign(x)|*cos(x)                         
                     |    2*cos (x)|       \                       \     sin (x) /                                                              /            \    sin(x)            /          6*cos(x)*sign(x)      
-6*DiracDelta(x) - 3*|1 + ---------|*|x| + ------------------------------------------------------------------------------------------------------------- - --------------------------------- + ---------------- + |x|
                     |        2    |                                                           sin(x)                                                                    sin(x)                     sin(x)           
                     \     sin (x) /
−3(1+2cos⁡2(x)sin⁡2(x))∣x∣−3(sign⁡(x)−cos⁡(x)∣x∣sin⁡(x))cos⁡(x)sin⁡(x)+(3(1+2cos⁡2(x)sin⁡2(x))sign⁡(x)−(5+6cos⁡2(x)sin⁡2(x))cos⁡(x)∣x∣sin⁡(x)+2δ(1)(x)−6cos⁡(x)δ(x)sin⁡(x))cos⁡(x)sin⁡(x)+∣x∣−6δ(x)+6cos⁡(x)sign⁡(x)sin⁡(x)- 3 \left(1 + \frac{2 \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) \left|{x}\right| - \frac{3 \left(\operatorname{sign}{\left(x \right)} - \frac{\cos{\left(x \right)} \left|{x}\right|}{\sin{\left(x \right)}}\right) \cos{\left(x \right)}}{\sin{\left(x \right)}} + \frac{\left(3 \left(1 + \frac{2 \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) \operatorname{sign}{\left(x \right)} - \frac{\left(5 + \frac{6 \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) \cos{\left(x \right)} \left|{x}\right|}{\sin{\left(x \right)}} + 2 \delta^{\left( 1 \right)}\left( x \right) - \frac{6 \cos{\left(x \right)} \delta\left(x\right)}{\sin{\left(x \right)}}\right) \cos{\left(x \right)}}{\sin{\left(x \right)}} + \left|{x}\right| - 6 \delta\left(x\right) + \frac{6 \cos{\left(x \right)} \operatorname{sign}{\left(x \right)}}{\sin{\left(x \right)}}
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