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Кореньarctgx/3
Derivada de la función/ arctg/ Кореньarctgx/3

Derivada de Кореньarctgx/3

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  _________  
\/ atan(x) *x
-------------
      3
xatan⁡(x)3\frac{x \sqrt{\operatorname{atan}{\left(x \right)}}}{3} 
(sqrt(atan(x))*x)/3
Gráfica
02468-8-6-4-2-101005
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
  _________                         
\/ atan(x)              x           
----------- + ----------------------
     3          /     2\   _________
              6*\1 + x /*\/ atan(x)
x6(x2+1)atan⁡(x)+atan⁡(x)3\frac{x}{6 \left(x^{2} + 1\right) \sqrt{\operatorname{atan}{\left(x \right)}}} + \frac{\sqrt{\operatorname{atan}{\left(x \right)}}}{3}
Simplificar
Segunda derivada [src] 
 /       /   1         \\ 
 |     x*|------- + 4*x|| 
 |       \atan(x)      /| 
-|-1 + -----------------| 
 |           /     2\   | 
 \         4*\1 + x /   / 
--------------------------
    /     2\   _________  
  3*\1 + x /*\/ atan(x)
−x(4x+1atan⁡(x))4(x2+1)−13(x2+1)atan⁡(x)- \frac{\frac{x \left(4 x + \frac{1}{\operatorname{atan}{\left(x \right)}}\right)}{4 \left(x^{2} + 1\right)} - 1}{3 \left(x^{2} + 1\right) \sqrt{\operatorname{atan}{\left(x \right)}}}
Simplificar
Tercera derivada [src] 
 /                    /                             2                    \\ 
 |                    |             3           32*x           12*x      || 
 |                  x*|-8 + ----------------- + ------ + ----------------|| 
 |                    |     /     2\     2           2   /     2\        || 
 |          3         \     \1 + x /*atan (x)   1 + x    \1 + x /*atan(x)/| 
-|3*x + --------- - ------------------------------------------------------| 
 \      4*atan(x)                             8                           / 
----------------------------------------------------------------------------
                                    2                                       
                            /     2\    _________                           
                          3*\1 + x / *\/ atan(x)
−−x(32x2x2+1+12x(x2+1)atan⁡(x)−8+3(x2+1)atan⁡2(x))8+3x+34atan⁡(x)3(x2+1)2atan⁡(x)- \frac{- \frac{x \left(\frac{32 x^{2}}{x^{2} + 1} + \frac{12 x}{\left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)}} - 8 + \frac{3}{\left(x^{2} + 1\right) \operatorname{atan}^{2}{\left(x \right)}}\right)}{8} + 3 x + \frac{3}{4 \operatorname{atan}{\left(x \right)}}}{3 \left(x^{2} + 1\right)^{2} \sqrt{\operatorname{atan}{\left(x \right)}}}
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Gráfico
Derivada de Кореньarctgx/3
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