Sr Examen

Otras calculadoras

y=(arcsin(x)-3x)/(√(x^2+1))
Derivada de la función/ y=(arcsin(x)-3x)/(√(x^2+1))

Derivada de y=(arcsin(x)-3x)/(√(x^2+1))

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
asin(x) - 3*x
-------------
    ________ 
   /  2      
 \/  x  + 1
−3x+asin⁡(x)x2+1\frac{- 3 x + \operatorname{asin}{\left(x \right)}}{\sqrt{x^{2} + 1}} 
(asin(x) - 3*x)/sqrt(x^2 + 1)
Gráfica
02468-8-6-4-2-10105-5
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
          1                         
-3 + -----------                    
        ________                    
       /      2                     
     \/  1 - x     x*(asin(x) - 3*x)
---------------- - -----------------
     ________                 3/2   
    /  2              / 2    \      
  \/  x  + 1          \x  + 1/
−x(−3x+asin⁡(x))(x2+1)32+−3+11−x2x2+1- \frac{x \left(- 3 x + \operatorname{asin}{\left(x \right)}\right)}{\left(x^{2} + 1\right)^{\frac{3}{2}}} + \frac{-3 + \frac{1}{\sqrt{1 - x^{2}}}}{\sqrt{x^{2} + 1}}
Simplificar
Segunda derivada [src] 
              /         2 \                        /         1     \
              |      3*x  |                    2*x*|3 - -----------|
              |-1 + ------|*(-asin(x) + 3*x)       |       ________|
              |          2|                        |      /      2 |
     x        \     1 + x /                        \    \/  1 - x  /
----------- - ------------------------------ + ---------------------
        3/2                    2                            2       
/     2\                  1 + x                        1 + x        
\1 - x /                                                            
--------------------------------------------------------------------
                               ________                             
                              /      2                              
                            \/  1 + x
2x(3−11−x2)x2+1+x(1−x2)32−(3x−asin⁡(x))(3x2x2+1−1)x2+1x2+1\frac{\frac{2 x \left(3 - \frac{1}{\sqrt{1 - x^{2}}}\right)}{x^{2} + 1} + \frac{x}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{\left(3 x - \operatorname{asin}{\left(x \right)}\right) \left(\frac{3 x^{2}}{x^{2} + 1} - 1\right)}{x^{2} + 1}}{\sqrt{x^{2} + 1}}
Simplificar
Tercera derivada [src] 
                                          /         2 \                                                       
            2                             |      3*x  | /         1     \       /         2 \                 
         3*x                            3*|-1 + ------|*|3 - -----------|       |      5*x  |                 
  -1 + -------                            |          2| |       ________|   3*x*|-3 + ------|*(-asin(x) + 3*x)
             2              2             \     1 + x / |      /      2 |       |          2|                 
       -1 + x            3*x                            \    \/  1 - x  /       \     1 + x /                 
- ------------ - -------------------- - --------------------------------- + ----------------------------------
          3/2                     3/2                      2                                    2             
  /     2\       /     2\ /     2\                    1 + x                             /     2\              
  \1 - x /       \1 + x /*\1 - x /                                                      \1 + x /              
--------------------------------------------------------------------------------------------------------------
                                                    ________                                                  
                                                   /      2                                                   
                                                 \/  1 + x
−3x2(1−x2)32(x2+1)+3x(3x−asin⁡(x))(5x2x2+1−3)(x2+1)2−3(3−11−x2)(3x2x2+1−1)x2+1−3x2x2−1−1(1−x2)32x2+1\frac{- \frac{3 x^{2}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \left(x^{2} + 1\right)} + \frac{3 x \left(3 x - \operatorname{asin}{\left(x \right)}\right) \left(\frac{5 x^{2}}{x^{2} + 1} - 3\right)}{\left(x^{2} + 1\right)^{2}} - \frac{3 \left(3 - \frac{1}{\sqrt{1 - x^{2}}}\right) \left(\frac{3 x^{2}}{x^{2} + 1} - 1\right)}{x^{2} + 1} - \frac{\frac{3 x^{2}}{x^{2} - 1} - 1}{\left(1 - x^{2}\right)^{\frac{3}{2}}}}{\sqrt{x^{2} + 1}}
Simplificar
Gráfico
Derivada de y=(arcsin(x)-3x)/(√(x^2+1))
    © Sr Examen – Калькулятор