Sr Examen

Otras calculadoras

atan(x-(sqrt(1+x^2)))
Derivada de la función/ 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
02468-8-6-4-2-10102-2
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}
Simplificar
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}
Simplificar
Tercera derivada [src] 
                                                                2                                                                           
                    3                        3 /       ________\                                             /        2  \ /       ________\
  /          x     \       /          x     \  |      /      2 |        /        2  \     /          x     \ |       x   | |      /      2 |
2*|-1 + -----------|     8*|-1 + -----------| *\x - \/  1 + x  /        |       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                                  2                      3/2                          /                     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}
Simplificar
Gráfico
Derivada de atan(x-(sqrt(1+x^2)))
    © Sr Examen – Калькулятор