Sr Examen

Otras calculadoras

(x*ln(2x+1)+arccos(5x))/((2x-1)^3+1)
Derivada de la función/ (x*ln(2x+1)+arccos(5x))/((2x-1)^3+1)

Derivada de (x*ln(2x+1)+arccos(5x))/((2x-1)^3+1)

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
x*log(2*x + 1) + acos(5*x)
--------------------------
               3          
      (2*x - 1)  + 1
xlog⁡(2x+1)+acos⁡(5x)(2x−1)3+1\frac{x \log{\left(2 x + 1 \right)} + \operatorname{acos}{\left(5 x \right)}}{\left(2 x - 1\right)^{3} + 1} 
(x*log(2*x + 1) + acos(5*x))/((2*x - 1)^3 + 1)
Gráfica
02468-8-6-4-2-1010-5050
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
        5            2*x                                                             
- -------------- + ------- + log(2*x + 1)                                            
     ___________   2*x + 1                                                           
    /         2                                        2                             
  \/  1 - 25*x                              6*(2*x - 1) *(x*log(2*x + 1) + acos(5*x))
----------------------------------------- - -----------------------------------------
                       3                                                2            
              (2*x - 1)  + 1                            /         3    \             
                                                        \(2*x - 1)  + 1/
−6(2x−1)2(xlog⁡(2x+1)+acos⁡(5x))((2x−1)3+1)2+2x2x+1+log⁡(2x+1)−51−25x2(2x−1)3+1- \frac{6 \left(2 x - 1\right)^{2} \left(x \log{\left(2 x + 1 \right)} + \operatorname{acos}{\left(5 x \right)}\right)}{\left(\left(2 x - 1\right)^{3} + 1\right)^{2}} + \frac{\frac{2 x}{2 x + 1} + \log{\left(2 x + 1 \right)} - \frac{5}{\sqrt{1 - 25 x^{2}}}}{\left(2 x - 1\right)^{3} + 1}
Simplificar
Segunda derivada [src] 
                                                     2 /        5            2*x                 \                 /                  3 \                             
                                        12*(-1 + 2*x) *|- -------------- + ------- + log(1 + 2*x)|                 |      3*(-1 + 2*x)  |                             
                                                       |     ___________   1 + 2*x               |   24*(-1 + 2*x)*|-1 + ---------------|*(x*log(1 + 2*x) + acos(5*x))
                                                       |    /         2                          |                 |                   3|                             
   4          125*x           4*x                      \  \/  1 - 25*x                           /                 \     1 + (-1 + 2*x) /                             
------- - -------------- - ---------- - ---------------------------------------------------------- + -----------------------------------------------------------------
1 + 2*x              3/2            2                                      3                                                                3                         
          /        2\      (1 + 2*x)                         1 + (-1 + 2*x)                                                   1 + (-1 + 2*x)                          
          \1 - 25*x /                                                                                                                                                 
----------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                         3                                                                            
                                                                           1 + (-1 + 2*x)
−4x(2x+1)2−125x(1−25x2)32−12(2x−1)2(2x2x+1+log⁡(2x+1)−51−25x2)(2x−1)3+1+24(2x−1)(xlog⁡(2x+1)+acos⁡(5x))(3(2x−1)3(2x−1)3+1−1)(2x−1)3+1+42x+1(2x−1)3+1\frac{- \frac{4 x}{\left(2 x + 1\right)^{2}} - \frac{125 x}{\left(1 - 25 x^{2}\right)^{\frac{3}{2}}} - \frac{12 \left(2 x - 1\right)^{2} \left(\frac{2 x}{2 x + 1} + \log{\left(2 x + 1 \right)} - \frac{5}{\sqrt{1 - 25 x^{2}}}\right)}{\left(2 x - 1\right)^{3} + 1} + \frac{24 \left(2 x - 1\right) \left(x \log{\left(2 x + 1 \right)} + \operatorname{acos}{\left(5 x \right)}\right) \left(\frac{3 \left(2 x - 1\right)^{3}}{\left(2 x - 1\right)^{3} + 1} - 1\right)}{\left(2 x - 1\right)^{3} + 1} + \frac{4}{2 x + 1}}{\left(2 x - 1\right)^{3} + 1}
Simplificar
Tercera derivada [src] 
                                                                                              /                  3                  6  \                                                                            /                  3 \                                            
                                                                                              |     18*(-1 + 2*x)      27*(-1 + 2*x)   |                2 /     4         4*x           125*x     \                 |      3*(-1 + 2*x)  | /        5            2*x                 \
                                                              48*(x*log(1 + 2*x) + acos(5*x))*|1 - --------------- + ------------------|   18*(-1 + 2*x) *|- ------- + ---------- + --------------|   72*(-1 + 2*x)*|-1 + ---------------|*|- -------------- + ------- + log(1 + 2*x)|
                                                                                              |                  3                    2|                  |  1 + 2*x            2              3/2|                 |                   3| |     ___________   1 + 2*x               |
                                         2                                                    |    1 + (-1 + 2*x)    /              3\ |                  |            (1 + 2*x)    /        2\   |                 \     1 + (-1 + 2*x) / |    /         2                          |
       125             12          9375*x           16*x                                      \                      \1 + (-1 + 2*x) / /                  \                         \1 - 25*x /   /                                        \  \/  1 - 25*x                           /
- -------------- - ---------- - -------------- + ---------- - -------------------------------------------------------------------------- + -------------------------------------------------------- + --------------------------------------------------------------------------------
             3/2            2              5/2            3                                              3                                                                   3                                                                      3                                 
  /        2\      (1 + 2*x)    /        2\      (1 + 2*x)                                 1 + (-1 + 2*x)                                                      1 + (-1 + 2*x)                                                         1 + (-1 + 2*x)                                  
  \1 - 25*x /                   \1 - 25*x /                                                                                                                                                                                                                                           
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                 3                                                                                                                                    
                                                                                                                                   1 + (-1 + 2*x)
−9375x2(1−25x2)52+16x(2x+1)3+18(2x−1)2(4x(2x+1)2+125x(1−25x2)32−42x+1)(2x−1)3+1+72(2x−1)(3(2x−1)3(2x−1)3+1−1)(2x2x+1+log⁡(2x+1)−51−25x2)(2x−1)3+1−48(xlog⁡(2x+1)+acos⁡(5x))(27(2x−1)6((2x−1)3+1)2−18(2x−1)3(2x−1)3+1+1)(2x−1)3+1−12(2x+1)2−125(1−25x2)32(2x−1)3+1\frac{- \frac{9375 x^{2}}{\left(1 - 25 x^{2}\right)^{\frac{5}{2}}} + \frac{16 x}{\left(2 x + 1\right)^{3}} + \frac{18 \left(2 x - 1\right)^{2} \left(\frac{4 x}{\left(2 x + 1\right)^{2}} + \frac{125 x}{\left(1 - 25 x^{2}\right)^{\frac{3}{2}}} - \frac{4}{2 x + 1}\right)}{\left(2 x - 1\right)^{3} + 1} + \frac{72 \left(2 x - 1\right) \left(\frac{3 \left(2 x - 1\right)^{3}}{\left(2 x - 1\right)^{3} + 1} - 1\right) \left(\frac{2 x}{2 x + 1} + \log{\left(2 x + 1 \right)} - \frac{5}{\sqrt{1 - 25 x^{2}}}\right)}{\left(2 x - 1\right)^{3} + 1} - \frac{48 \left(x \log{\left(2 x + 1 \right)} + \operatorname{acos}{\left(5 x \right)}\right) \left(\frac{27 \left(2 x - 1\right)^{6}}{\left(\left(2 x - 1\right)^{3} + 1\right)^{2}} - \frac{18 \left(2 x - 1\right)^{3}}{\left(2 x - 1\right)^{3} + 1} + 1\right)}{\left(2 x - 1\right)^{3} + 1} - \frac{12}{\left(2 x + 1\right)^{2}} - \frac{125}{\left(1 - 25 x^{2}\right)^{\frac{3}{2}}}}{\left(2 x - 1\right)^{3} + 1}
Simplificar
Gráfico
Derivada de (x*ln(2x+1)+arccos(5x))/((2x-1)^3+1)
    © Sr Examen – Калькулятор