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y=\arctan\sqrt(x^(2)-1)
Derivada de la función/ x^(2)/ arctan/ y=\arctan\sqrt(x^(2)-1)

Derivada de y=\arctan\sqrt(x^(2)-1)

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

Gráfico:

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Solución

Ha introducido [src] 
  atan(x)  
-----------
   ________
  /  2     
\/  x  - 1
atan⁡(x)x2−1\frac{\operatorname{atan}{\left(x \right)}}{\sqrt{x^{2} - 1}} 
atan(x)/sqrt(x^2 - 1)
Gráfica
02468-8-6-4-2-1010-1010
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Trazar el gráfico f'(x)
Primera derivada [src] 
         1              x*atan(x) 
-------------------- - -----------
            ________           3/2
/     2\   /  2        / 2    \   
\1 + x /*\/  x  - 1    \x  - 1/
−xatan⁡(x)(x2−1)32+1x2−1(x2+1)- \frac{x \operatorname{atan}{\left(x \right)}}{\left(x^{2} - 1\right)^{\frac{3}{2}}} + \frac{1}{\sqrt{x^{2} - 1} \left(x^{2} + 1\right)}
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Segunda derivada [src] 
              /          2 \                             
              |       3*x  |                             
              |-1 + -------|*atan(x)                     
              |           2|                             
     2*x      \     -1 + x /                  2*x        
- --------- + ---------------------- - ------------------
          2                2           /     2\ /      2\
  /     2\           -1 + x            \1 + x /*\-1 + x /
  \1 + x /                                               
---------------------------------------------------------
                          _________                      
                         /       2                       
                       \/  -1 + x
−2x(x2+1)2−2x(x2−1)(x2+1)+(3x2x2−1−1)atan⁡(x)x2−1x2−1\frac{- \frac{2 x}{\left(x^{2} + 1\right)^{2}} - \frac{2 x}{\left(x^{2} - 1\right) \left(x^{2} + 1\right)} + \frac{\left(\frac{3 x^{2}}{x^{2} - 1} - 1\right) \operatorname{atan}{\left(x \right)}}{x^{2} - 1}}{\sqrt{x^{2} - 1}}
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Tercera derivada [src] 
  /         2 \      /          2 \                              /          2 \        
  |      4*x  |      |       3*x  |                              |       5*x  |        
2*|-1 + ------|    3*|-1 + -------|                          3*x*|-3 + -------|*atan(x)
  |          2|      |           2|               2              |           2|        
  \     1 + x /      \     -1 + x /            6*x               \     -1 + x /        
--------------- + ------------------ + ------------------- - --------------------------
           2      /     2\ /      2\           2                              2        
   /     2\       \1 + x /*\-1 + x /   /     2\  /      2\           /      2\         
   \1 + x /                            \1 + x / *\-1 + x /           \-1 + x /         
---------------------------------------------------------------------------------------
                                         _________                                     
                                        /       2                                      
                                      \/  -1 + x
6x2(x2−1)(x2+1)2−3x(5x2x2−1−3)atan⁡(x)(x2−1)2+2(4x2x2+1−1)(x2+1)2+3(3x2x2−1−1)(x2−1)(x2+1)x2−1\frac{\frac{6 x^{2}}{\left(x^{2} - 1\right) \left(x^{2} + 1\right)^{2}} - \frac{3 x \left(\frac{5 x^{2}}{x^{2} - 1} - 3\right) \operatorname{atan}{\left(x \right)}}{\left(x^{2} - 1\right)^{2}} + \frac{2 \left(\frac{4 x^{2}}{x^{2} + 1} - 1\right)}{\left(x^{2} + 1\right)^{2}} + \frac{3 \left(\frac{3 x^{2}}{x^{2} - 1} - 1\right)}{\left(x^{2} - 1\right) \left(x^{2} + 1\right)}}{\sqrt{x^{2} - 1}}
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Gráfico
Derivada de y=\arctan\sqrt(x^(2)-1)
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