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y=(arctg^3)*(sqrtsinx)

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  • Derivada de:
  • Derivada de i*n*x
  • Derivada de 3^-x Derivada de 3^-x
  • Derivada de y=6x Derivada de y=6x
  • Derivada de 25/x Derivada de 25/x

  • Expresiones idénticas

  • y=(arctg^ tres)*(sqrtsinx)
  • y es igual a (arctg al cubo ) multiplicar por ( raíz cuadrada de seno de x)
  • y es igual a (arctg en el grado tres) multiplicar por ( raíz cuadrada de seno de x)
  • y=(arctg^3)*(√sinx)
  • y=(arctg3)*(sqrtsinx)
  • y=arctg3*sqrtsinx
  • y=(arctg³)*(sqrtsinx)
  • y=(arctg en el grado 3)*(sqrtsinx)
  • y=(arctg^3)(sqrtsinx)
  • y=(arctg3)(sqrtsinx)
  • y=arctg3sqrtsinx
  • y=arctg^3sqrtsinx
Derivada de la función/ arctg/ sqrtsinx/ y=(arctg^3)*(sqrtsinx)

Derivada de y=(arctg^3)*(sqrtsinx)

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
    3      ________
atan (x)*\/ sin(x)
sin⁡(x)atan⁡3(x)\sqrt{\sin{\left(x \right)}} \operatorname{atan}^{3}{\left(x \right)} 
atan(x)^3*sqrt(sin(x))
Gráfica
02468-8-6-4-2-1010-2020
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Trazar el gráfico f'(x)
Primera derivada [src] 
    3                   2      ________
atan (x)*cos(x)   3*atan (x)*\/ sin(x) 
--------------- + ---------------------
      ________                 2       
  2*\/ sin(x)             1 + x
cos⁡(x)atan⁡3(x)2sin⁡(x)+3sin⁡(x)atan⁡2(x)x2+1\frac{\cos{\left(x \right)} \operatorname{atan}^{3}{\left(x \right)}}{2 \sqrt{\sin{\left(x \right)}}} + \frac{3 \sqrt{\sin{\left(x \right)}} \operatorname{atan}^{2}{\left(x \right)}}{x^{2} + 1}
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Segunda derivada [src] 
/           /                   2    \                                                      \        
|      2    |    ________    cos (x) |                                                      |        
|  atan (x)*|2*\/ sin(x)  + ---------|                                                      |        
|           |                  3/2   |       ________                                       |        
|           \               sin   (x)/   6*\/ sin(x) *(-1 + x*atan(x))     3*atan(x)*cos(x) |        
|- ----------------------------------- - ----------------------------- + -------------------|*atan(x)
|                   4                                      2             /     2\   ________|        
|                                                  /     2\              \1 + x /*\/ sin(x) |        
\                                                  \1 + x /                                 /
(−(2sin⁡(x)+cos⁡2(x)sin⁡32(x))atan⁡2(x)4+3cos⁡(x)atan⁡(x)(x2+1)sin⁡(x)−6(xatan⁡(x)−1)sin⁡(x)(x2+1)2)atan⁡(x)\left(- \frac{\left(2 \sqrt{\sin{\left(x \right)}} + \frac{\cos^{2}{\left(x \right)}}{\sin^{\frac{3}{2}}{\left(x \right)}}\right) \operatorname{atan}^{2}{\left(x \right)}}{4} + \frac{3 \cos{\left(x \right)} \operatorname{atan}{\left(x \right)}}{\left(x^{2} + 1\right) \sqrt{\sin{\left(x \right)}}} - \frac{6 \left(x \operatorname{atan}{\left(x \right)} - 1\right) \sqrt{\sin{\left(x \right)}}}{\left(x^{2} + 1\right)^{2}}\right) \operatorname{atan}{\left(x \right)}
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Tercera derivada [src] 
             /                                     2     2   \              /                   2    \            /         2   \                                           
    ________ |  1          2      6*x*atan(x)   4*x *atan (x)|         2    |    ________    cos (x) |       3    |    3*cos (x)|                                           
6*\/ sin(x) *|------ - atan (x) - ----------- + -------------|   9*atan (x)*|2*\/ sin(x)  + ---------|   atan (x)*|2 + ---------|*cos(x)                                    
             |     2                      2              2   |              |                  3/2   |            |        2    |                                           
             \1 + x                  1 + x          1 + x    /              \               sin   (x)/            \     sin (x) /          9*(-1 + x*atan(x))*atan(x)*cos(x)
-------------------------------------------------------------- - ------------------------------------- + ------------------------------- - ---------------------------------
                                  2                                              /     2\                              ________                           2                 
                          /     2\                                             4*\1 + x /                          8*\/ sin(x)                    /     2\    ________      
                          \1 + x /                                                                                                                \1 + x / *\/ sin(x)
(2+3cos⁡2(x)sin⁡2(x))cos⁡(x)atan⁡3(x)8sin⁡(x)−9(2sin⁡(x)+cos⁡2(x)sin⁡32(x))atan⁡2(x)4(x2+1)−9(xatan⁡(x)−1)cos⁡(x)atan⁡(x)(x2+1)2sin⁡(x)+6(4x2atan⁡2(x)x2+1−6xatan⁡(x)x2+1−atan⁡2(x)+1x2+1)sin⁡(x)(x2+1)2\frac{\left(2 + \frac{3 \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) \cos{\left(x \right)} \operatorname{atan}^{3}{\left(x \right)}}{8 \sqrt{\sin{\left(x \right)}}} - \frac{9 \left(2 \sqrt{\sin{\left(x \right)}} + \frac{\cos^{2}{\left(x \right)}}{\sin^{\frac{3}{2}}{\left(x \right)}}\right) \operatorname{atan}^{2}{\left(x \right)}}{4 \left(x^{2} + 1\right)} - \frac{9 \left(x \operatorname{atan}{\left(x \right)} - 1\right) \cos{\left(x \right)} \operatorname{atan}{\left(x \right)}}{\left(x^{2} + 1\right)^{2} \sqrt{\sin{\left(x \right)}}} + \frac{6 \left(\frac{4 x^{2} \operatorname{atan}^{2}{\left(x \right)}}{x^{2} + 1} - \frac{6 x \operatorname{atan}{\left(x \right)}}{x^{2} + 1} - \operatorname{atan}^{2}{\left(x \right)} + \frac{1}{x^{2} + 1}\right) \sqrt{\sin{\left(x \right)}}}{\left(x^{2} + 1\right)^{2}}
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Gráfico
Derivada de y=(arctg^3)*(sqrtsinx)
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