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atan(x+sqrt(1+x^2))
Derivada de la función/ 1+x^2/ (x+sqrt(1+x^2))/ atan(x+sqrt(1+x^2))

Derivada de atan(x+sqrt(1+x^2))

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
    /       ________\
    |      /      2 |
atan\x + \/  1 + x  /
atan⁡(x+x2+1)\operatorname{atan}{\left(x + \sqrt{x^{2} + 1} \right)} 
atan(x + sqrt(1 + x^2))
Gráfica
02468-8-6-4-2-101002
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
            x         
   1 + -----------    
          ________    
         /      2     
       \/  1 + x      
----------------------
                     2
    /       ________\ 
    |      /      2 | 
1 + \x + \/  1 + x  /
xx2+1+1(x+x2+1)2+1\frac{\frac{x}{\sqrt{x^{2} + 1}} + 1}{\left(x + \sqrt{x^{2} + 1}\right)^{2} + 1}
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Segunda derivada [src] 
 /                                 2 /       ________\\ 
 |        2       /         x     \  |      /      2 || 
 |       x      2*|1 + -----------| *\x + \/  1 + x  /| 
 |-1 + ------     |       ________|                   | 
 |          2     |      /      2 |                   | 
 |     1 + x      \    \/  1 + x  /                   | 
-|----------- + --------------------------------------| 
 |   ________                                2        | 
 |  /      2                /       ________\         | 
 |\/  1 + x                 |      /      2 |         | 
 \                      1 + \x + \/  1 + x  /         / 
--------------------------------------------------------
                                      2                 
                     /       ________\                  
                     |      /      2 |                  
                 1 + \x + \/  1 + x  /
−2(x+x2+1)(xx2+1+1)2(x+x2+1)2+1+x2x2+1−1x2+1(x+x2+1)2+1- \frac{\frac{2 \left(x + \sqrt{x^{2} + 1}\right) \left(\frac{x}{\sqrt{x^{2} + 1}} + 1\right)^{2}}{\left(x + \sqrt{x^{2} + 1}\right)^{2} + 1} + \frac{\frac{x^{2}}{x^{2} + 1} - 1}{\sqrt{x^{2} + 1}}}{\left(x + \sqrt{x^{2} + 1}\right)^{2} + 1}
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Tercera derivada [src] 
                                                                                     2                                                      
                      3                                           3 /       ________\                        /        2  \ /       ________\
     /         x     \         /        2  \     /         x     \  |      /      2 |      /         x     \ |       x   | |      /      2 |
   2*|1 + -----------|         |       x   |   8*|1 + -----------| *\x + \/  1 + x  /    6*|1 + -----------|*|-1 + ------|*\x + \/  1 + x  /
     |       ________|     3*x*|-1 + ------|     |       ________|                         |       ________| |          2|                  
     |      /      2 |         |          2|     |      /      2 |                         |      /      2 | \     1 + x /                  
     \    \/  1 + x  /         \     1 + x /     \    \/  1 + x  /                         \    \/  1 + x  /                                
- ---------------------- + ----------------- + --------------------------------------- + ---------------------------------------------------
                       2              3/2                                     2                              /                     2\       
      /       ________\       /     2\                /                     2\                      ________ |    /       ________\ |       
      |      /      2 |       \1 + x /                |    /       ________\ |                     /      2  |    |      /      2 | |       
  1 + \x + \/  1 + x  /                               |    |      /      2 | |                   \/  1 + x  *\1 + \x + \/  1 + x  / /       
                                                      \1 + \x + \/  1 + x  / /                                                              
--------------------------------------------------------------------------------------------------------------------------------------------
                                                                                2                                                           
                                                               /       ________\                                                            
                                                               |      /      2 |                                                            
                                                           1 + \x + \/  1 + x  /
3x(x2x2+1−1)(x2+1)32+8(x+x2+1)2(xx2+1+1)3((x+x2+1)2+1)2+6(x+x2+1)(xx2+1+1)(x2x2+1−1)x2+1((x+x2+1)2+1)−2(xx2+1+1)3(x+x2+1)2+1(x+x2+1)2+1\frac{\frac{3 x \left(\frac{x^{2}}{x^{2} + 1} - 1\right)}{\left(x^{2} + 1\right)^{\frac{3}{2}}} + \frac{8 \left(x + \sqrt{x^{2} + 1}\right)^{2} \left(\frac{x}{\sqrt{x^{2} + 1}} + 1\right)^{3}}{\left(\left(x + \sqrt{x^{2} + 1}\right)^{2} + 1\right)^{2}} + \frac{6 \left(x + \sqrt{x^{2} + 1}\right) \left(\frac{x}{\sqrt{x^{2} + 1}} + 1\right) \left(\frac{x^{2}}{x^{2} + 1} - 1\right)}{\sqrt{x^{2} + 1} \left(\left(x + \sqrt{x^{2} + 1}\right)^{2} + 1\right)} - \frac{2 \left(\frac{x}{\sqrt{x^{2} + 1}} + 1\right)^{3}}{\left(x + \sqrt{x^{2} + 1}\right)^{2} + 1}}{\left(x + \sqrt{x^{2} + 1}\right)^{2} + 1}
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Gráfico
Derivada de atan(x+sqrt(1+x^2))
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