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Derivada de la función/ arctg/ 2-x^2/ y=arctg*(x)/sqrt(a^2-x^2)

Derivada de y=arctg*(x)/sqrt(a^2-x^2)

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

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Solución

Ha introducido [src] 
  atan(x)   
------------
   _________
  /  2    2 
\/  a  - x
atan⁡(x)a2−x2\frac{\operatorname{atan}{\left(x \right)}}{\sqrt{a^{2} - x^{2}}} 
atan(x)/sqrt(a^2 - x^2)
Primera derivada [src] 
          1              x*atan(x)  
--------------------- + ------------
            _________            3/2
/     2\   /  2    2    / 2    2\   
\1 + x /*\/  a  - x     \a  - x /
xatan⁡(x)(a2−x2)32+1a2−x2(x2+1)\frac{x \operatorname{atan}{\left(x \right)}}{\left(a^{2} - x^{2}\right)^{\frac{3}{2}}} + \frac{1}{\sqrt{a^{2} - x^{2}} \left(x^{2} + 1\right)}
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Segunda derivada [src] 
              /         2 \                             
              |      3*x  |                             
              |1 + -------|*atan(x)                     
              |     2    2|                             
     2*x      \    a  - x /                  2*x        
- --------- + --------------------- + ------------------
          2           2    2          /     2\ / 2    2\
  /     2\           a  - x           \1 + x /*\a  - x /
  \1 + x /                                              
--------------------------------------------------------
                         _________                      
                        /  2    2                       
                      \/  a  - x
−2x(x2+1)2+2x(a2−x2)(x2+1)+(3x2a2−x2+1)atan⁡(x)a2−x2a2−x2\frac{- \frac{2 x}{\left(x^{2} + 1\right)^{2}} + \frac{2 x}{\left(a^{2} - x^{2}\right) \left(x^{2} + 1\right)} + \frac{\left(\frac{3 x^{2}}{a^{2} - x^{2}} + 1\right) \operatorname{atan}{\left(x \right)}}{a^{2} - x^{2}}}{\sqrt{a^{2} - x^{2}}}
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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|         |     2    2|        
  \     1 + x /           6*x              \    a  - x /         \    a  - x /        
--------------- - ------------------- + ------------------ + -------------------------
           2              2             /     2\ / 2    2\                    2       
   /     2\       /     2\  / 2    2\   \1 + x /*\a  - x /           / 2    2\        
   \1 + x /       \1 + x / *\a  - x /                                \a  - x /        
--------------------------------------------------------------------------------------
                                        _________                                     
                                       /  2    2                                      
                                     \/  a  - x
−6x2(a2−x2)(x2+1)2+3x(5x2a2−x2+3)atan⁡(x)(a2−x2)2+2(4x2x2+1−1)(x2+1)2+3(3x2a2−x2+1)(a2−x2)(x2+1)a2−x2\frac{- \frac{6 x^{2}}{\left(a^{2} - x^{2}\right) \left(x^{2} + 1\right)^{2}} + \frac{3 x \left(\frac{5 x^{2}}{a^{2} - x^{2}} + 3\right) \operatorname{atan}{\left(x \right)}}{\left(a^{2} - x^{2}\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}}{a^{2} - x^{2}} + 1\right)}{\left(a^{2} - x^{2}\right) \left(x^{2} + 1\right)}}{\sqrt{a^{2} - x^{2}}}
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