Sr Examen

Otras calculadoras

Derivada de la función/ 3sqrt/ x-lnx/ arctg/ ctg2x/ y=3sqrtarctg2x-lnx/1+2x

Derivada de y=3sqrtarctg2x-lnx/1+2x

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
    ___________   log(x)      
3*\/ atan(2*x)  - ------ + 2*x
                    1
$$2 x + \left(- \frac{\log{\left(x \right)}}{1} + 3 \sqrt{\operatorname{atan}{\left(2 x \right)}}\right)$$ 
3*sqrt(atan(2*x)) - log(x)/1 + 2*x
Gráfica
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
    1              3            
2 - - + ------------------------
    x   /       2\   ___________
        \1 + 4*x /*\/ atan(2*x)
$$2 + \frac{3}{\left(4 x^{2} + 1\right) \sqrt{\operatorname{atan}{\left(2 x \right)}}} - \frac{1}{x}$$
Simplificar
Segunda derivada [src] 
1               3                          24*x          
-- - ------------------------ - -------------------------
 2             2                          2              
x    /       2\      3/2        /       2\    ___________
     \1 + 4*x / *atan   (2*x)   \1 + 4*x / *\/ atan(2*x)
$$- \frac{24 x}{\left(4 x^{2} + 1\right)^{2} \sqrt{\operatorname{atan}{\left(2 x \right)}}} - \frac{3}{\left(4 x^{2} + 1\right)^{2} \operatorname{atan}^{\frac{3}{2}}{\left(2 x \right)}} + \frac{1}{x^{2}}$$
Simplificar
Tercera derivada [src] 
                                                                                                        2         
  2                24                         9                         72*x                       384*x          
- -- - ------------------------- + ------------------------ + ------------------------ + -------------------------
   3             2                           3                          3                          3              
  x    /       2\    ___________   /       2\      5/2        /       2\      3/2        /       2\    ___________
       \1 + 4*x / *\/ atan(2*x)    \1 + 4*x / *atan   (2*x)   \1 + 4*x / *atan   (2*x)   \1 + 4*x / *\/ atan(2*x)
$$\frac{384 x^{2}}{\left(4 x^{2} + 1\right)^{3} \sqrt{\operatorname{atan}{\left(2 x \right)}}} + \frac{72 x}{\left(4 x^{2} + 1\right)^{3} \operatorname{atan}^{\frac{3}{2}}{\left(2 x \right)}} - \frac{24}{\left(4 x^{2} + 1\right)^{2} \sqrt{\operatorname{atan}{\left(2 x \right)}}} + \frac{9}{\left(4 x^{2} + 1\right)^{3} \operatorname{atan}^{\frac{5}{2}}{\left(2 x \right)}} - \frac{2}{x^{3}}$$
Simplificar
    © Sr Examen