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xsin5x/(arctg^2(3x))

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  • Derivada de:
  • Derivada de 5^10 Derivada de 5^10
  • Derivada de i*n*sin(x)
  • Derivada de √2x Derivada de √2x
  • Derivada de 3^-x Derivada de 3^-x

  • Expresiones idénticas

  • xsin5x/(arctg^ dos (3x))
  • x seno de 5x dividir por (arctg al cuadrado (3x))
  • x seno de 5x dividir por (arctg en el grado dos (3x))
  • xsin5x/(arctg2(3x))
  • xsin5x/arctg23x
  • xsin5x/(arctg²(3x))
  • xsin5x/(arctg en el grado 2(3x))
  • xsin5x/arctg^23x
  • xsin5x dividir por (arctg^2(3x))
Derivada de la función/ ctg^2/ sin5x/ xsin5/ arctg/ tg^2(3x)/ xsin5x/(arctg^2(3x))

Derivada de xsin5x/(arctg^2(3x))

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
x*sin(5*x)
----------
    2     
atan (3*x)
xsin⁡(5x)atan⁡2(3x)\frac{x \sin{\left(5 x \right)}}{\operatorname{atan}^{2}{\left(3 x \right)}} 
(x*sin(5*x))/atan(3*x)^2
Gráfica
02468-8-6-4-2-1010-5050
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
5*x*cos(5*x) + sin(5*x)        6*x*sin(5*x)    
----------------------- - ---------------------
           2              /       2\     3     
       atan (3*x)         \1 + 9*x /*atan (3*x)
−6xsin⁡(5x)(9x2+1)atan⁡3(3x)+5xcos⁡(5x)+sin⁡(5x)atan⁡2(3x)- \frac{6 x \sin{\left(5 x \right)}}{\left(9 x^{2} + 1\right) \operatorname{atan}^{3}{\left(3 x \right)}} + \frac{5 x \cos{\left(5 x \right)} + \sin{\left(5 x \right)}}{\operatorname{atan}^{2}{\left(3 x \right)}}
Simplificar
Segunda derivada [src] 
                                                                  /    1          \         
                                                             54*x*|--------- + 2*x|*sin(5*x)
                              12*(5*x*cos(5*x) + sin(5*x))        \atan(3*x)      /         
10*cos(5*x) - 25*x*sin(5*x) - ---------------------------- + -------------------------------
                                  /       2\                                2               
                                  \1 + 9*x /*atan(3*x)            /       2\                
                                                                  \1 + 9*x / *atan(3*x)     
--------------------------------------------------------------------------------------------
                                             2                                              
                                         atan (3*x)
54x(2x+1atan⁡(3x))sin⁡(5x)(9x2+1)2atan⁡(3x)−25xsin⁡(5x)+10cos⁡(5x)−12(5xcos⁡(5x)+sin⁡(5x))(9x2+1)atan⁡(3x)atan⁡2(3x)\frac{\frac{54 x \left(2 x + \frac{1}{\operatorname{atan}{\left(3 x \right)}}\right) \sin{\left(5 x \right)}}{\left(9 x^{2} + 1\right)^{2} \operatorname{atan}{\left(3 x \right)}} - 25 x \sin{\left(5 x \right)} + 10 \cos{\left(5 x \right)} - \frac{12 \left(5 x \cos{\left(5 x \right)} + \sin{\left(5 x \right)}\right)}{\left(9 x^{2} + 1\right) \operatorname{atan}{\left(3 x \right)}}}{\operatorname{atan}^{2}{\left(3 x \right)}}
Simplificar
Tercera derivada [src] 
                                                                                                                          /                                  2                         \         
                                                                                                                          |               6              36*x              27*x        |         
                                                                      /    1          \                             108*x*|-1 + --------------------- + -------- + --------------------|*sin(5*x)
                                                                  162*|--------- + 2*x|*(5*x*cos(5*x) + sin(5*x))         |     /       2\     2               2   /       2\          |         
                                90*(-2*cos(5*x) + 5*x*sin(5*x))       \atan(3*x)      /                                   \     \1 + 9*x /*atan (3*x)   1 + 9*x    \1 + 9*x /*atan(3*x)/         
-75*sin(5*x) - 125*x*cos(5*x) + ------------------------------- + ----------------------------------------------- - -----------------------------------------------------------------------------
                                      /       2\                                         2                                                                2                                      
                                      \1 + 9*x /*atan(3*x)                     /       2\                                                       /       2\                                       
                                                                               \1 + 9*x / *atan(3*x)                                            \1 + 9*x / *atan(3*x)                            
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                2                                                                                                
                                                                                            atan (3*x)
−125xcos⁡(5x)−108x(36x29x2+1+27x(9x2+1)atan⁡(3x)−1+6(9x2+1)atan⁡2(3x))sin⁡(5x)(9x2+1)2atan⁡(3x)+162(2x+1atan⁡(3x))(5xcos⁡(5x)+sin⁡(5x))(9x2+1)2atan⁡(3x)−75sin⁡(5x)+90(5xsin⁡(5x)−2cos⁡(5x))(9x2+1)atan⁡(3x)atan⁡2(3x)\frac{- 125 x \cos{\left(5 x \right)} - \frac{108 x \left(\frac{36 x^{2}}{9 x^{2} + 1} + \frac{27 x}{\left(9 x^{2} + 1\right) \operatorname{atan}{\left(3 x \right)}} - 1 + \frac{6}{\left(9 x^{2} + 1\right) \operatorname{atan}^{2}{\left(3 x \right)}}\right) \sin{\left(5 x \right)}}{\left(9 x^{2} + 1\right)^{2} \operatorname{atan}{\left(3 x \right)}} + \frac{162 \left(2 x + \frac{1}{\operatorname{atan}{\left(3 x \right)}}\right) \left(5 x \cos{\left(5 x \right)} + \sin{\left(5 x \right)}\right)}{\left(9 x^{2} + 1\right)^{2} \operatorname{atan}{\left(3 x \right)}} - 75 \sin{\left(5 x \right)} + \frac{90 \left(5 x \sin{\left(5 x \right)} - 2 \cos{\left(5 x \right)}\right)}{\left(9 x^{2} + 1\right) \operatorname{atan}{\left(3 x \right)}}}{\operatorname{atan}^{2}{\left(3 x \right)}}
Simplificar
Gráfico
Derivada de xsin5x/(arctg^2(3x))
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