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  • Derivada de:
  • Derivada de (x-1)^2 Derivada de (x-1)^2
  • Derivada de 4 Derivada de 4
  • Derivada de 2/x^3 Derivada de 2/x^3
  • Derivada de -2 Derivada de -2

  • Expresiones idénticas

  • y=x/sqrt(x^ dos cos^2*x)
  • y es igual a x dividir por raíz cuadrada de (x al cuadrado coseno de al cuadrado multiplicar por x)
  • y es igual a x dividir por raíz cuadrada de (x en el grado dos coseno de al cuadrado multiplicar por x)
  • y=x/√(x^2cos^2*x)
  • y=x/sqrt(x2cos2*x)
  • y=x/sqrtx2cos2*x
  • y=x/sqrt(x²cos²*x)
  • y=x/sqrt(x en el grado 2cos en el grado 2*x)
  • y=x/sqrt(x^2cos^2x)
  • y=x/sqrt(x2cos2x)
  • y=x/sqrtx2cos2x
  • y=x/sqrtx^2cos^2x
  • y=x dividir por sqrt(x^2cos^2*x)

  • Expresiones con funciones

  • Raíz cuadrada sqrt
  • sqrt(x^2)
  • sqrt(x^5)
  • sqrt(x-1)
  • sqrt(x)*x
  • sqrt(x^2-6x+13)
Derivada de la función/ cos^2/ x/sqrt(x^2cos^2*x)/ y=x/sqrt(x^2cos^2*x)

Derivada de y=x/sqrt(x^2cos^2*x)

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
       x       
---------------
   ____________
  /  2    2    
\/  x *cos (x)
xx2cos⁡2(x)\frac{x}{\sqrt{x^{2} \cos^{2}{\left(x \right)}}} 
x/sqrt(x^2*cos(x)^2)
Primera derivada [src] 
                       2       2              
       1          x*cos (x) - x *cos(x)*sin(x)
--------------- - ----------------------------
   ____________                        2      
  /  2    2          x*|x|*|cos(x)|*cos (x)   
\/  x *cos (x)
1x2cos⁡2(x)−−x2sin⁡(x)cos⁡(x)+xcos⁡2(x)xcos⁡2(x)∣x∣∣cos⁡(x)∣\frac{1}{\sqrt{x^{2} \cos^{2}{\left(x \right)}}} - \frac{- x^{2} \sin{\left(x \right)} \cos{\left(x \right)} + x \cos^{2}{\left(x \right)}}{x \cos^{2}{\left(x \right)} \left|{x}\right| \left|{\cos{\left(x \right)}}\right|}
Simplificar
Segunda derivada [src] 
                                                                2       2    2       2    2                                                       
                     /    sign(x)     sign(cos(x))*sin(x)\   cos (x) + x *sin (x) - x *cos (x) - 4*x*cos(x)*sin(x)   2*(-cos(x) + x*sin(x))*sin(x)
(-cos(x) + x*sin(x))*|- ----------- + -------------------| - ----------------------------------------------------- + -----------------------------
                     |   2                       2       |                   x*|x|*|cos(x)|*cos(x)                        |x|*|cos(x)|*cos(x)     
                     \  x *|cos(x)|       |x|*cos (x)    /                                                                                        
--------------------------------------------------------------------------------------------------------------------------------------------------
                                                                      cos(x)
(xsin⁡(x)−cos⁡(x))(sin⁡(x)sign⁡(cos⁡(x))cos⁡2(x)∣x∣−sign⁡(x)x2∣cos⁡(x)∣)+2(xsin⁡(x)−cos⁡(x))sin⁡(x)cos⁡(x)∣x∣∣cos⁡(x)∣−x2sin⁡2(x)−x2cos⁡2(x)−4xsin⁡(x)cos⁡(x)+cos⁡2(x)xcos⁡(x)∣x∣∣cos⁡(x)∣cos⁡(x)\frac{\left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \left(\frac{\sin{\left(x \right)} \operatorname{sign}{\left(\cos{\left(x \right)} \right)}}{\cos^{2}{\left(x \right)} \left|{x}\right|} - \frac{\operatorname{sign}{\left(x \right)}}{x^{2} \left|{\cos{\left(x \right)}}\right|}\right) + \frac{2 \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \sin{\left(x \right)}}{\cos{\left(x \right)} \left|{x}\right| \left|{\cos{\left(x \right)}}\right|} - \frac{x^{2} \sin^{2}{\left(x \right)} - x^{2} \cos^{2}{\left(x \right)} - 4 x \sin{\left(x \right)} \cos{\left(x \right)} + \cos^{2}{\left(x \right)}}{x \cos{\left(x \right)} \left|{x}\right| \left|{\cos{\left(x \right)}}\right|}}{\cos{\left(x \right)}}
Simplificar
Tercera derivada [src] 
                                                                                                                                                                    /                                                                                         2       2    2       2    2                                                       \                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    
                                                                                                                                                                    |                     /    sign(x)     sign(cos(x))*sin(x)\   2*(-cos(x) + x*sin(x))   cos (x) + x *sin (x) - x *cos (x) - 4*x*cos(x)*sin(x)   2*(-cos(x) + x*sin(x))*sin(x)|                          /    sign(x)     sign(cos(x))*sin(x)\                            /    sign(x)     sign(cos(x))*sin(x)\ /   2       2    2       2    2                       \                                                           /    sign(x)     sign(cos(x))*sin(x)\                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            
                                                                                                                                                                  3*|(-cos(x) + x*sin(x))*|- ----------- + -------------------| - ---------------------- - ----------------------------------------------------- + -----------------------------|   2*(-cos(x) + x*sin(x))*|- ----------- + -------------------|                            |- ----------- + -------------------|*\cos (x) + x *sin (x) - x *cos (x) - 4*x*cos(x)*sin(x)/                                    2*(-cos(x) + x*sin(x))*|- ----------- + -------------------|*sin(x)                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     
                       /                                                      2                        2                                                      \     |                     |   2                       2       |       x*|x|*|cos(x)|                       x*|x|*|cos(x)|*cos(x)                        |x|*|cos(x)|*cos(x)     |                          |   2                       2       |                            |   2                       2       |                                                                                                                   |   2                       2       |                                   /   2       2    2       2    2                       \             /         2                               2         2              \        2                                          /   2       2    2       2    2                       \        2                           /   2       2    2       2    2                       \                                                         /   2       2    2       2    2                       \                                                                                            
                       |  sign(cos(x))    2*sign(x)    2*DiracDelta(x)   2*sin (x)*sign(cos(x))   2*sin (x)*DiracDelta(cos(x))   2*sign(x)*sign(cos(x))*sin(x)|     \                     \  x *|cos(x)|       |x|*cos (x)    /                                                                                                                 /                          \  x *|cos(x)|       |x|*cos (x)    /   2*(-cos(x) + x*sin(x))   \  x *|cos(x)|       |x|*cos (x)    /                                                           2*(-cos(x) + x*sin(x))*sign(x)                          \  x *|cos(x)|       |x|*cos (x)    /          6*(-cos(x) + x*sin(x))   \cos (x) + x *sin (x) - x *cos (x) - 4*x*cos(x)*sin(x)/*sign(x)   2*\- 3*x*cos (x) - 3*cos(x)*sin(x) + 3*x*sin (x) + 2*x *cos(x)*sin(x)/   2*sin (x)*(-cos(x) + x*sin(x))*sign(cos(x))   4*\cos (x) + x *sin (x) - x *cos (x) - 4*x*cos(x)*sin(x)/   6*sin (x)*(-cos(x) + x*sin(x))   \cos (x) + x *sin (x) - x *cos (x) - 4*x*cos(x)*sin(x)/*sign(cos(x))*sin(x)   8*(-cos(x) + x*sin(x))*sin(x)   4*\cos (x) + x *sin (x) - x *cos (x) - 4*x*cos(x)*sin(x)/*sin(x)   2*(-cos(x) + x*sin(x))*sign(cos(x))*sin(x)   2*(-cos(x) + x*sin(x))*sign(x)*sin(x)
- (-cos(x) + x*sin(x))*|- ------------ - ----------- + --------------- - ---------------------- + ---------------------------- + -----------------------------| + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------ + ---------------------- - --------------------------------------------------------------------------------------------- + ------------------------------ + ------------------------------------------------------------------- + ---------------------- + --------------------------------------------------------------- - ---------------------------------------------------------------------- + ------------------------------------------- + --------------------------------------------------------- + ------------------------------ - --------------------------------------------------------------------------- - ----------------------------- - ---------------------------------------------------------------- - ------------------------------------------ - -------------------------------------
                       |   |x|*cos(x)     3               2                          3                           2                          2    2            |                                                                                          x                                                                                                                       x                                      |x|*|cos(x)|                                                   x*cos(x)                                                       3                                                     cos(x)                                     2                                            3                                                                 x*|x|*|cos(x)|*cos(x)                                                   3                                         2                                                             2                                                   3                                         x*|x|*|cos(x)|*cos(x)                                              2                                                  2                                2                         
                       \                 x *|cos(x)|     x *|cos(x)|          |x|*cos (x)                 |x|*cos (x)                      x *cos (x)         /                                                                                                                                                                                                                                                                                                                                                                                      x *|cos(x)|                                                                                      x *|x|*|cos(x)|                              x *|cos(x)|*cos(x)                                                                                                                  |x|*cos (x)                                     x *|x|*|cos(x)|*cos(x)                         |x|*|cos(x)|*cos (x)                                       x*|x|*cos (x)                                                                                       x*|x|*|cos(x)|*cos (x)                                      x*|x|*cos (x)                            x *|cos(x)|*cos(x)         
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                cos(x)
2(xsin⁡(x)−cos⁡(x))(sin⁡(x)sign⁡(cos⁡(x))cos⁡2(x)∣x∣−sign⁡(x)x2∣cos⁡(x)∣)sin⁡(x)cos⁡(x)−(xsin⁡(x)−cos⁡(x))(2sin⁡2(x)δ(cos⁡(x))cos⁡2(x)∣x∣−2sin⁡2(x)sign⁡(cos⁡(x))cos⁡3(x)∣x∣−sign⁡(cos⁡(x))cos⁡(x)∣x∣+2sin⁡(x)sign⁡(x)sign⁡(cos⁡(x))x2cos⁡2(x)+2δ(x)x2∣cos⁡(x)∣−2sign⁡(x)x3∣cos⁡(x)∣)+6(xsin⁡(x)−cos⁡(x))sin⁡2(x)cos⁡2(x)∣x∣∣cos⁡(x)∣+2(xsin⁡(x)−cos⁡(x))sin⁡2(x)sign⁡(cos⁡(x))cos⁡3(x)∣x∣+2(xsin⁡(x)−cos⁡(x))∣x∣∣cos⁡(x)∣−2(xsin⁡(x)−cos⁡(x))(sin⁡(x)sign⁡(cos⁡(x))cos⁡2(x)∣x∣−sign⁡(x)x2∣cos⁡(x)∣)x−8(xsin⁡(x)−cos⁡(x))sin⁡(x)xcos⁡(x)∣x∣∣cos⁡(x)∣−2(xsin⁡(x)−cos⁡(x))sin⁡(x)sign⁡(cos⁡(x))xcos⁡2(x)∣x∣−(sin⁡(x)sign⁡(cos⁡(x))cos⁡2(x)∣x∣−sign⁡(x)x2∣cos⁡(x)∣)(x2sin⁡2(x)−x2cos⁡2(x)−4xsin⁡(x)cos⁡(x)+cos⁡2(x))xcos⁡(x)−4(x2sin⁡2(x)−x2cos⁡2(x)−4xsin⁡(x)cos⁡(x)+cos⁡2(x))sin⁡(x)xcos⁡2(x)∣x∣∣cos⁡(x)∣−(x2sin⁡2(x)−x2cos⁡2(x)−4xsin⁡(x)cos⁡(x)+cos⁡2(x))sin⁡(x)sign⁡(cos⁡(x))xcos⁡3(x)∣x∣+3((xsin⁡(x)−cos⁡(x))(sin⁡(x)sign⁡(cos⁡(x))cos⁡2(x)∣x∣−sign⁡(x)x2∣cos⁡(x)∣)+2(xsin⁡(x)−cos⁡(x))sin⁡(x)cos⁡(x)∣x∣∣cos⁡(x)∣−2(xsin⁡(x)−cos⁡(x))x∣x∣∣cos⁡(x)∣−x2sin⁡2(x)−x2cos⁡2(x)−4xsin⁡(x)cos⁡(x)+cos⁡2(x)xcos⁡(x)∣x∣∣cos⁡(x)∣)x−2(2x2sin⁡(x)cos⁡(x)+3xsin⁡2(x)−3xcos⁡2(x)−3sin⁡(x)cos⁡(x))xcos⁡(x)∣x∣∣cos⁡(x)∣−2(xsin⁡(x)−cos⁡(x))sin⁡(x)sign⁡(x)x2cos⁡(x)∣cos⁡(x)∣+6(xsin⁡(x)−cos⁡(x))x2∣x∣∣cos⁡(x)∣+4(x2sin⁡2(x)−x2cos⁡2(x)−4xsin⁡(x)cos⁡(x)+cos⁡2(x))x2cos⁡(x)∣x∣∣cos⁡(x)∣+2(xsin⁡(x)−cos⁡(x))sign⁡(x)x3∣cos⁡(x)∣+(x2sin⁡2(x)−x2cos⁡2(x)−4xsin⁡(x)cos⁡(x)+cos⁡2(x))sign⁡(x)x3cos⁡(x)∣cos⁡(x)∣cos⁡(x)\frac{\frac{2 \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \left(\frac{\sin{\left(x \right)} \operatorname{sign}{\left(\cos{\left(x \right)} \right)}}{\cos^{2}{\left(x \right)} \left|{x}\right|} - \frac{\operatorname{sign}{\left(x \right)}}{x^{2} \left|{\cos{\left(x \right)}}\right|}\right) \sin{\left(x \right)}}{\cos{\left(x \right)}} - \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \left(\frac{2 \sin^{2}{\left(x \right)} \delta\left(\cos{\left(x \right)}\right)}{\cos^{2}{\left(x \right)} \left|{x}\right|} - \frac{2 \sin^{2}{\left(x \right)} \operatorname{sign}{\left(\cos{\left(x \right)} \right)}}{\cos^{3}{\left(x \right)} \left|{x}\right|} - \frac{\operatorname{sign}{\left(\cos{\left(x \right)} \right)}}{\cos{\left(x \right)} \left|{x}\right|} + \frac{2 \sin{\left(x \right)} \operatorname{sign}{\left(x \right)} \operatorname{sign}{\left(\cos{\left(x \right)} \right)}}{x^{2} \cos^{2}{\left(x \right)}} + \frac{2 \delta\left(x\right)}{x^{2} \left|{\cos{\left(x \right)}}\right|} - \frac{2 \operatorname{sign}{\left(x \right)}}{x^{3} \left|{\cos{\left(x \right)}}\right|}\right) + \frac{6 \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)} \left|{x}\right| \left|{\cos{\left(x \right)}}\right|} + \frac{2 \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \sin^{2}{\left(x \right)} \operatorname{sign}{\left(\cos{\left(x \right)} \right)}}{\cos^{3}{\left(x \right)} \left|{x}\right|} + \frac{2 \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right)}{\left|{x}\right| \left|{\cos{\left(x \right)}}\right|} - \frac{2 \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \left(\frac{\sin{\left(x \right)} \operatorname{sign}{\left(\cos{\left(x \right)} \right)}}{\cos^{2}{\left(x \right)} \left|{x}\right|} - \frac{\operatorname{sign}{\left(x \right)}}{x^{2} \left|{\cos{\left(x \right)}}\right|}\right)}{x} - \frac{8 \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \sin{\left(x \right)}}{x \cos{\left(x \right)} \left|{x}\right| \left|{\cos{\left(x \right)}}\right|} - \frac{2 \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \sin{\left(x \right)} \operatorname{sign}{\left(\cos{\left(x \right)} \right)}}{x \cos^{2}{\left(x \right)} \left|{x}\right|} - \frac{\left(\frac{\sin{\left(x \right)} \operatorname{sign}{\left(\cos{\left(x \right)} \right)}}{\cos^{2}{\left(x \right)} \left|{x}\right|} - \frac{\operatorname{sign}{\left(x \right)}}{x^{2} \left|{\cos{\left(x \right)}}\right|}\right) \left(x^{2} \sin^{2}{\left(x \right)} - x^{2} \cos^{2}{\left(x \right)} - 4 x \sin{\left(x \right)} \cos{\left(x \right)} + \cos^{2}{\left(x \right)}\right)}{x \cos{\left(x \right)}} - \frac{4 \left(x^{2} \sin^{2}{\left(x \right)} - x^{2} \cos^{2}{\left(x \right)} - 4 x \sin{\left(x \right)} \cos{\left(x \right)} + \cos^{2}{\left(x \right)}\right) \sin{\left(x \right)}}{x \cos^{2}{\left(x \right)} \left|{x}\right| \left|{\cos{\left(x \right)}}\right|} - \frac{\left(x^{2} \sin^{2}{\left(x \right)} - x^{2} \cos^{2}{\left(x \right)} - 4 x \sin{\left(x \right)} \cos{\left(x \right)} + \cos^{2}{\left(x \right)}\right) \sin{\left(x \right)} \operatorname{sign}{\left(\cos{\left(x \right)} \right)}}{x \cos^{3}{\left(x \right)} \left|{x}\right|} + \frac{3 \left(\left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \left(\frac{\sin{\left(x \right)} \operatorname{sign}{\left(\cos{\left(x \right)} \right)}}{\cos^{2}{\left(x \right)} \left|{x}\right|} - \frac{\operatorname{sign}{\left(x \right)}}{x^{2} \left|{\cos{\left(x \right)}}\right|}\right) + \frac{2 \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \sin{\left(x \right)}}{\cos{\left(x \right)} \left|{x}\right| \left|{\cos{\left(x \right)}}\right|} - \frac{2 \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right)}{x \left|{x}\right| \left|{\cos{\left(x \right)}}\right|} - \frac{x^{2} \sin^{2}{\left(x \right)} - x^{2} \cos^{2}{\left(x \right)} - 4 x \sin{\left(x \right)} \cos{\left(x \right)} + \cos^{2}{\left(x \right)}}{x \cos{\left(x \right)} \left|{x}\right| \left|{\cos{\left(x \right)}}\right|}\right)}{x} - \frac{2 \left(2 x^{2} \sin{\left(x \right)} \cos{\left(x \right)} + 3 x \sin^{2}{\left(x \right)} - 3 x \cos^{2}{\left(x \right)} - 3 \sin{\left(x \right)} \cos{\left(x \right)}\right)}{x \cos{\left(x \right)} \left|{x}\right| \left|{\cos{\left(x \right)}}\right|} - \frac{2 \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \sin{\left(x \right)} \operatorname{sign}{\left(x \right)}}{x^{2} \cos{\left(x \right)} \left|{\cos{\left(x \right)}}\right|} + \frac{6 \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right)}{x^{2} \left|{x}\right| \left|{\cos{\left(x \right)}}\right|} + \frac{4 \left(x^{2} \sin^{2}{\left(x \right)} - x^{2} \cos^{2}{\left(x \right)} - 4 x \sin{\left(x \right)} \cos{\left(x \right)} + \cos^{2}{\left(x \right)}\right)}{x^{2} \cos{\left(x \right)} \left|{x}\right| \left|{\cos{\left(x \right)}}\right|} + \frac{2 \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \operatorname{sign}{\left(x \right)}}{x^{3} \left|{\cos{\left(x \right)}}\right|} + \frac{\left(x^{2} \sin^{2}{\left(x \right)} - x^{2} \cos^{2}{\left(x \right)} - 4 x \sin{\left(x \right)} \cos{\left(x \right)} + \cos^{2}{\left(x \right)}\right) \operatorname{sign}{\left(x \right)}}{x^{3} \cos{\left(x \right)} \left|{\cos{\left(x \right)}}\right|}}{\cos{\left(x \right)}}
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