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x/sqrt2arctg(x/sqrt2)
Derivada de la función/ arctg/ sqrt2/ x/sqrt2arctg(x/sqrt2)

Derivada de x/sqrt2arctg(x/sqrt2)

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

Gráfico:

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Solución

Ha introducido [src] 
         x          
--------------------
     _______________
    /       /  x  \ 
   /  2*atan|-----| 
  /         |  ___| 
\/          \\/ 2 /
x2atan⁡(x2)\frac{x}{\sqrt{2 \operatorname{atan}{\left(\frac{x}{\sqrt{2}} \right)}}} 
x/sqrt(2*atan(x/sqrt(2)))
Gráfica
02468-8-6-4-2-1010010
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
         1                         x            
-------------------- - -------------------------
     _______________     /     2\               
    /       /  x  \      |    x |     3/2/  x  \
   /  2*atan|-----|    4*|1 + --|*atan   |-----|
  /         |  ___|      \    2 /        |  ___|
\/          \\/ 2 /                      \\/ 2 /
−x4(x22+1)atan⁡32(x2)+12atan⁡(x2)- \frac{x}{4 \left(\frac{x^{2}}{2} + 1\right) \operatorname{atan}^{\frac{3}{2}}{\left(\frac{x}{\sqrt{2}} \right)}} + \frac{1}{\sqrt{2 \operatorname{atan}{\left(\frac{x}{\sqrt{2}} \right)}}}
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Segunda derivada [src] 
       /             ___   \
       |         3*\/ 2    |
     x*|4*x + -------------|
       |          /    ___\|
       |          |x*\/ 2 ||
       |      atan|-------||
       \          \   2   //
-4 + -----------------------
                   2        
              2 + x         
----------------------------
                  /    ___\ 
  /     2\     3/2|x*\/ 2 | 
4*\2 + x /*atan   |-------| 
                  \   2   /
x(4x+32atan⁡(2x2))x2+2−44(x2+2)atan⁡32(2x2)\frac{\frac{x \left(4 x + \frac{3 \sqrt{2}}{\operatorname{atan}{\left(\frac{\sqrt{2} x}{2} \right)}}\right)}{x^{2} + 2} - 4}{4 \left(x^{2} + 2\right) \operatorname{atan}^{\frac{3}{2}}{\left(\frac{\sqrt{2} x}{2} \right)}}
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Tercera derivada [src] 
         /                                   2                 ___      \          ___   
         |                15             16*x           18*x*\/ 2       |      9*\/ 2    
12*x - x*|-4 + ----------------------- + ------ + ----------------------| + -------------
         |                   /    ___\        2                /    ___\|       /    ___\
         |     /     2\     2|x*\/ 2 |   2 + x    /     2\     |x*\/ 2 ||       |x*\/ 2 |
         |     \2 + x /*atan |-------|            \2 + x /*atan|-------||   atan|-------|
         \                   \   2   /                         \   2   //       \   2   /
-----------------------------------------------------------------------------------------
                                         2        /    ___\                              
                                 /     2\      3/2|x*\/ 2 |                              
                               4*\2 + x / *atan   |-------|                              
                                                  \   2   /
−x(16x2x2+2+182x(x2+2)atan⁡(2x2)−4+15(x2+2)atan⁡2(2x2))+12x+92atan⁡(2x2)4(x2+2)2atan⁡32(2x2)\frac{- x \left(\frac{16 x^{2}}{x^{2} + 2} + \frac{18 \sqrt{2} x}{\left(x^{2} + 2\right) \operatorname{atan}{\left(\frac{\sqrt{2} x}{2} \right)}} - 4 + \frac{15}{\left(x^{2} + 2\right) \operatorname{atan}^{2}{\left(\frac{\sqrt{2} x}{2} \right)}}\right) + 12 x + \frac{9 \sqrt{2}}{\operatorname{atan}{\left(\frac{\sqrt{2} x}{2} \right)}}}{4 \left(x^{2} + 2\right)^{2} \operatorname{atan}^{\frac{3}{2}}{\left(\frac{\sqrt{2} x}{2} \right)}}
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Gráfico
Derivada de x/sqrt2arctg(x/sqrt2)
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