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Derivada de la función/ (x^2)/ y=ln(cosx/sqrt(x^2))

Derivada de y=ln(cosx/sqrt(x^2))

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

Ha introducido [src] 
   / cos(x)\
log|-------|
   |   ____|
   |  /  2 |
   \\/  x  /
log⁡(cos⁡(x)x2)\log{\left(\frac{\cos{\left(x \right)}}{\sqrt{x^{2}}} \right)} 
log(cos(x)/sqrt(x^2))
Primera derivada [src] 
/  sin(x)   cos(x)\    
|- ------ - ------|*|x|
\   |x|     x*|x| /    
-----------------------
         cos(x)
(−sin⁡(x)∣x∣−cos⁡(x)x∣x∣)∣x∣cos⁡(x)\frac{\left(- \frac{\sin{\left(x \right)}}{\left|{x}\right|} - \frac{\cos{\left(x \right)}}{x \left|{x}\right|}\right) \left|{x}\right|}{\cos{\left(x \right)}}
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Segunda derivada [src] 
                                                                     /cos(x)         \           /cos(x)         \       
                                                                     |------ + sin(x)|*sign(x)   |------ + sin(x)|*sin(x)
/  cos(x)   sin(x)   cos(x)*sign(x)   cos(x)   sign(x)*sin(x)\       \  x            /           \  x            /       
|- ------ + ------ + -------------- + ------ + --------------|*|x| - ------------------------- - ------------------------
|   |x|     x*|x|           3          2              2      |                  |x|                       cos(x)         
\                          x          x *|x|         x       /                                                           
-------------------------------------------------------------------------------------------------------------------------
                                                          cos(x)
−(sin⁡(x)+cos⁡(x)x)sin⁡(x)cos⁡(x)−(sin⁡(x)+cos⁡(x)x)sign⁡(x)∣x∣+(−cos⁡(x)∣x∣+sin⁡(x)x∣x∣+sin⁡(x)sign⁡(x)x2+cos⁡(x)x2∣x∣+cos⁡(x)sign⁡(x)x3)∣x∣cos⁡(x)\frac{- \frac{\left(\sin{\left(x \right)} + \frac{\cos{\left(x \right)}}{x}\right) \sin{\left(x \right)}}{\cos{\left(x \right)}} - \frac{\left(\sin{\left(x \right)} + \frac{\cos{\left(x \right)}}{x}\right) \operatorname{sign}{\left(x \right)}}{\left|{x}\right|} + \left(- \frac{\cos{\left(x \right)}}{\left|{x}\right|} + \frac{\sin{\left(x \right)}}{x \left|{x}\right|} + \frac{\sin{\left(x \right)} \operatorname{sign}{\left(x \right)}}{x^{2}} + \frac{\cos{\left(x \right)}}{x^{2} \left|{x}\right|} + \frac{\cos{\left(x \right)} \operatorname{sign}{\left(x \right)}}{x^{3}}\right) \left|{x}\right|}{\cos{\left(x \right)}}
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Tercera derivada [src] 
                                                                                                                                                                                                                                                                                                                           /  cos(x)   sin(x)   cos(x)*sign(x)   cos(x)   sign(x)*sin(x)\                                                
                                                                                                                                                                                                                                                         /cos(x)         \                      2    /cos(x)         \   2*|- ------ + ------ + -------------- + ------ + --------------|*|x|*sin(x)     /cos(x)         \               
                                                                                                                                                                                                                                                       2*|------ + sin(x)|*DiracDelta(x)   2*sin (x)*|------ + sin(x)|     |   |x|     x*|x|           3          2              2      |              2*|------ + sin(x)|*sign(x)*sin(x)
          /sin(x)   cos(x)   4*cos(x)*sign(x)   4*sign(x)*sin(x)   2*cos(x)   2*sin(x)   2*DiracDelta(x)*cos(x)   2*DiracDelta(x)*sin(x)   2*cos(x)*sign(x)\       cos(x)     /  cos(x)   sin(x)   cos(x)*sign(x)   cos(x)   sign(x)*sin(x)\             \  x            /                           \  x            /     \                          x          x *|x|         x       /                \  x            /               
-sin(x) + |------ + ------ - ---------------- - ---------------- - -------- - -------- + ---------------------- + ---------------------- + ----------------|*|x| - ------ + 2*|- ------ + ------ + -------------- + ------ + --------------|*sign(x) - --------------------------------- - --------------------------- + --------------------------------------------------------------------------- - ----------------------------------
          | |x|     x*|x|            4                  3            3          2                   3                        2                     2       |         x        |   |x|     x*|x|           3          2              2      |                          |x|                               2                                                   cos(x)                                                 |x|*cos(x)            
          \                         x                  x            x *|x|     x *|x|              x                        x                     x        /                  \                          x          x *|x|         x       /                                                         cos (x)                                                                                                                             
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                                                                                  cos(x)
−2(sin⁡(x)+cos⁡(x)x)sin⁡2(x)cos⁡2(x)−2(sin⁡(x)+cos⁡(x)x)sin⁡(x)sign⁡(x)cos⁡(x)∣x∣−2(sin⁡(x)+cos⁡(x)x)δ(x)∣x∣+2(−cos⁡(x)∣x∣+sin⁡(x)x∣x∣+sin⁡(x)sign⁡(x)x2+cos⁡(x)x2∣x∣+cos⁡(x)sign⁡(x)x3)sin⁡(x)∣x∣cos⁡(x)+2(−cos⁡(x)∣x∣+sin⁡(x)x∣x∣+sin⁡(x)sign⁡(x)x2+cos⁡(x)x2∣x∣+cos⁡(x)sign⁡(x)x3)sign⁡(x)+(sin⁡(x)∣x∣+cos⁡(x)x∣x∣+2sin⁡(x)δ(x)x2−2sin⁡(x)x2∣x∣+2cos⁡(x)sign⁡(x)x2−4sin⁡(x)sign⁡(x)x3+2cos⁡(x)δ(x)x3−2cos⁡(x)x3∣x∣−4cos⁡(x)sign⁡(x)x4)∣x∣−sin⁡(x)−cos⁡(x)xcos⁡(x)\frac{- \frac{2 \left(\sin{\left(x \right)} + \frac{\cos{\left(x \right)}}{x}\right) \sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} - \frac{2 \left(\sin{\left(x \right)} + \frac{\cos{\left(x \right)}}{x}\right) \sin{\left(x \right)} \operatorname{sign}{\left(x \right)}}{\cos{\left(x \right)} \left|{x}\right|} - \frac{2 \left(\sin{\left(x \right)} + \frac{\cos{\left(x \right)}}{x}\right) \delta\left(x\right)}{\left|{x}\right|} + \frac{2 \left(- \frac{\cos{\left(x \right)}}{\left|{x}\right|} + \frac{\sin{\left(x \right)}}{x \left|{x}\right|} + \frac{\sin{\left(x \right)} \operatorname{sign}{\left(x \right)}}{x^{2}} + \frac{\cos{\left(x \right)}}{x^{2} \left|{x}\right|} + \frac{\cos{\left(x \right)} \operatorname{sign}{\left(x \right)}}{x^{3}}\right) \sin{\left(x \right)} \left|{x}\right|}{\cos{\left(x \right)}} + 2 \left(- \frac{\cos{\left(x \right)}}{\left|{x}\right|} + \frac{\sin{\left(x \right)}}{x \left|{x}\right|} + \frac{\sin{\left(x \right)} \operatorname{sign}{\left(x \right)}}{x^{2}} + \frac{\cos{\left(x \right)}}{x^{2} \left|{x}\right|} + \frac{\cos{\left(x \right)} \operatorname{sign}{\left(x \right)}}{x^{3}}\right) \operatorname{sign}{\left(x \right)} + \left(\frac{\sin{\left(x \right)}}{\left|{x}\right|} + \frac{\cos{\left(x \right)}}{x \left|{x}\right|} + \frac{2 \sin{\left(x \right)} \delta\left(x\right)}{x^{2}} - \frac{2 \sin{\left(x \right)}}{x^{2} \left|{x}\right|} + \frac{2 \cos{\left(x \right)} \operatorname{sign}{\left(x \right)}}{x^{2}} - \frac{4 \sin{\left(x \right)} \operatorname{sign}{\left(x \right)}}{x^{3}} + \frac{2 \cos{\left(x \right)} \delta\left(x\right)}{x^{3}} - \frac{2 \cos{\left(x \right)}}{x^{3} \left|{x}\right|} - \frac{4 \cos{\left(x \right)} \operatorname{sign}{\left(x \right)}}{x^{4}}\right) \left|{x}\right| - \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{x}}{\cos{\left(x \right)}}
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