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atan(x)*sqrt(x^2-1)
Derivada de la función/ x^2-1/ tan(x)/ atan(x)*sqrt(x^2-1)

Derivada de atan(x)*sqrt(x^2-1)

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

Gráfico:

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Solución

Ha introducido [src] 
           ________
          /  2     
atan(x)*\/  x  - 1
x2−1atan⁡(x)\sqrt{x^{2} - 1} \operatorname{atan}{\left(x \right)} 
atan(x)*sqrt(x^2 - 1)
Gráfica
02468-8-6-4-2-1010-5050
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
   ________              
  /  2                   
\/  x  - 1     x*atan(x) 
----------- + -----------
        2        ________
   1 + x        /  2     
              \/  x  - 1
xatan⁡(x)x2−1+x2−1x2+1\frac{x \operatorname{atan}{\left(x \right)}}{\sqrt{x^{2} - 1}} + \frac{\sqrt{x^{2} - 1}}{x^{2} + 1}
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Segunda derivada [src] 
  /         2  \                                                   
  |        x   |                                                   
  |-1 + -------|*atan(x)          _________                        
  |           2|                 /       2                         
  \     -1 + x /           2*x*\/  -1 + x              2*x         
- ---------------------- - ---------------- + ---------------------
          _________                   2                   _________
         /       2            /     2\        /     2\   /       2 
       \/  -1 + x             \1 + x /        \1 + x /*\/  -1 + x
−2xx2−1(x2+1)2+2xx2−1(x2+1)−(x2x2−1−1)atan⁡(x)x2−1- \frac{2 x \sqrt{x^{2} - 1}}{\left(x^{2} + 1\right)^{2}} + \frac{2 x}{\sqrt{x^{2} - 1} \left(x^{2} + 1\right)} - \frac{\left(\frac{x^{2}}{x^{2} - 1} - 1\right) \operatorname{atan}{\left(x \right)}}{\sqrt{x^{2} - 1}}
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Tercera derivada [src] 
                                /         2  \          _________ /         2 \       /         2  \        
                                |        x   |         /       2  |      4*x  |       |        x   |        
                              3*|-1 + -------|     2*\/  -1 + x  *|-1 + ------|   3*x*|-1 + -------|*atan(x)
              2                 |           2|                    |          2|       |           2|        
           6*x                  \     -1 + x /                    \     1 + x /       \     -1 + x /        
- ---------------------- - --------------------- + ---------------------------- + --------------------------
          2    _________               _________                    2                             3/2       
  /     2\    /       2    /     2\   /       2             /     2\                     /      2\          
  \1 + x / *\/  -1 + x     \1 + x /*\/  -1 + x              \1 + x /                     \-1 + x /
−6x2x2−1(x2+1)2+3x(x2x2−1−1)atan⁡(x)(x2−1)32+2x2−1(4x2x2+1−1)(x2+1)2−3(x2x2−1−1)x2−1(x2+1)- \frac{6 x^{2}}{\sqrt{x^{2} - 1} \left(x^{2} + 1\right)^{2}} + \frac{3 x \left(\frac{x^{2}}{x^{2} - 1} - 1\right) \operatorname{atan}{\left(x \right)}}{\left(x^{2} - 1\right)^{\frac{3}{2}}} + \frac{2 \sqrt{x^{2} - 1} \left(\frac{4 x^{2}}{x^{2} + 1} - 1\right)}{\left(x^{2} + 1\right)^{2}} - \frac{3 \left(\frac{x^{2}}{x^{2} - 1} - 1\right)}{\sqrt{x^{2} - 1} \left(x^{2} + 1\right)}
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Gráfico
Derivada de atan(x)*sqrt(x^2-1)
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