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  • Derivada de (3x+6)^2 Derivada de (3x+6)^2
  • Derivada de 2*y-4 Derivada de 2*y-4
  • Derivada de 2*cos(x)/sin(x) Derivada de 2*cos(x)/sin(x)
  • Derivada de (-2)/cos(x) Derivada de (-2)/cos(x)

  • Expresiones idénticas

  • (x(sqrt(x))- tres x)/(dos (sqrt(x^ tres))+(x^ dos)^(uno /3))
  • (x( raíz cuadrada de (x)) menos 3x) dividir por (2( raíz cuadrada de (x al cubo )) más (x al cuadrado ) en el grado (1 dividir por 3))
  • (x( raíz cuadrada de (x)) menos tres x) dividir por (dos ( raíz cuadrada de (x en el grado tres)) más (x en el grado dos) en el grado (uno dividir por 3))
  • (x(√(x))-3x)/(2(√(x^3))+(x^2)^(1/3))
  • (x(sqrt(x))-3x)/(2(sqrt(x3))+(x2)(1/3))
  • xsqrtx-3x/2sqrtx3+x21/3
  • (x(sqrt(x))-3x)/(2(sqrt(x³))+(x²)^(1/3))
  • (x(sqrt(x))-3x)/(2(sqrt(x en el grado 3))+(x en el grado 2) en el grado (1/3))
  • xsqrtx-3x/2sqrtx^3+x^2^1/3
  • (x(sqrt(x))-3x) dividir por (2(sqrt(x^3))+(x^2)^(1 dividir por 3))

  • Expresiones semejantes

  • (x(sqrt(x))+3x)/(2(sqrt(x^3))+(x^2)^(1/3))
  • (x(sqrt(x))-3x)/(2(sqrt(x^3))-(x^2)^(1/3))
Derivada de la función/ (x(sqrt(x))-3x)/(2(sqrt(x^3))+(x^2)^(1/3))

Derivada de (x(sqrt(x))-3x)/(2(sqrt(x^3))+(x^2)^(1/3))

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
       ___         
   x*\/ x  - 3*x   
-------------------
     ____      ____
    /  3    3 /  2 
2*\/  x   + \/  x
xx−3x2x3+x23\frac{\sqrt{x} x - 3 x}{2 \sqrt{x^{3}} + \sqrt[3]{x^{2}}} 
(x*sqrt(x) - 3*x)/(2*sqrt(x^3) + (x^2)^(1/3))
Primera derivada [src] 
                                      /       ____           \
             ___                      |      /  3         2/3|
         3*\/ x       /    ___      \ |  3*\/  x     2*|x|   |
    -3 + -------      \x*\/ x  - 3*x/*|- --------- - --------|
            2                         \      x         3*x   /
------------------- + ----------------------------------------
     ____      ____                                 2         
    /  3    3 /  2             /     ____      ____\          
2*\/  x   + \/  x              |    /  3    3 /  2 |          
                               \2*\/  x   + \/  x  /
3x2−32x3+x23+(−3x3x−2∣x∣233x)(xx−3x)(2x3+x23)2\frac{\frac{3 \sqrt{x}}{2} - 3}{2 \sqrt{x^{3}} + \sqrt[3]{x^{2}}} + \frac{\left(- \frac{3 \sqrt{x^{3}}}{x} - \frac{2 \left|{x}\right|^{\frac{2}{3}}}{3 x}\right) \left(\sqrt{x} x - 3 x\right)}{\left(2 \sqrt{x^{3}} + \sqrt[3]{x^{2}}\right)^{2}}
Simplificar
Segunda derivada [src] 
                                                             /                                                               2\
                                                             |                                ____     /                ____\ |
                                                             |        2/3                    /  3      |     2/3       /  3 | |
                                                / 3/2      \ |  12*|x|      8*sign(x)   27*\/  x     4*\2*|x|    + 9*\/  x  / |
                                                \x    - 3*x/*|- --------- + --------- + ---------- - -------------------------|
                       /                ____\                |      x        3 _____        x            /              ____\ |
          /       ___\ |     2/3       /  3 |                |               \/ |x|                      |   2/3       /  3 | |
   3      \-2 + \/ x /*\2*|x|    + 9*\/  x  /                \                                         x*\|x|    + 2*\/  x  / /
------- - ----------------------------------- - -------------------------------------------------------------------------------
    ___            /              ____\                                         /              ____\                           
4*\/ x             |   2/3       /  3 |                                         |   2/3       /  3 |                           
                 x*\|x|    + 2*\/  x  /                                    18*x*\|x|    + 2*\/  x  /                           
-------------------------------------------------------------------------------------------------------------------------------
                                                                     ____                                                      
                                                          2/3       /  3                                                       
                                                       |x|    + 2*\/  x
−(x−2)(9x3+2∣x∣23)x(2x3+∣x∣23)−(x32−3x)(8sign⁡(x)∣x∣3+27x3x−12∣x∣23x−4(9x3+2∣x∣23)2x(2x3+∣x∣23))18x(2x3+∣x∣23)+34x2x3+∣x∣23\frac{- \frac{\left(\sqrt{x} - 2\right) \left(9 \sqrt{x^{3}} + 2 \left|{x}\right|^{\frac{2}{3}}\right)}{x \left(2 \sqrt{x^{3}} + \left|{x}\right|^{\frac{2}{3}}\right)} - \frac{\left(x^{\frac{3}{2}} - 3 x\right) \left(\frac{8 \operatorname{sign}{\left(x \right)}}{\sqrt[3]{\left|{x}\right|}} + \frac{27 \sqrt{x^{3}}}{x} - \frac{12 \left|{x}\right|^{\frac{2}{3}}}{x} - \frac{4 \left(9 \sqrt{x^{3}} + 2 \left|{x}\right|^{\frac{2}{3}}\right)^{2}}{x \left(2 \sqrt{x^{3}} + \left|{x}\right|^{\frac{2}{3}}\right)}\right)}{18 x \left(2 \sqrt{x^{3}} + \left|{x}\right|^{\frac{2}{3}}\right)} + \frac{3}{4 \sqrt{x}}}{2 \sqrt{x^{3}} + \left|{x}\right|^{\frac{2}{3}}}
Simplificar
Tercera derivada [src] 
                                                                                                                                          /                                                                                                                                 /                                ____\\
                                                                                                                                          |                                                                                                          /                ____\ |        2/3                    /  3 ||
                                                                                                                                          |                                                                                      3                   |     2/3       /  3 | |  12*|x|      8*sign(x)   27*\/  x  ||
                                                      /                                                               2\                  |                                                      ____      /                ____\                 12*\2*|x|    + 9*\/  x  /*|- --------- + --------- + ----------||
                                                      |                                ____     /                ____\ |                  |         2/3                             2           /  3       |     2/3       /  3 |                                           |      x        3 _____        x     ||
                                                      |        2/3                    /  3      |     2/3       /  3 | |     / 3/2      \ |  144*|x|      96*DiracDelta(x)   16*sign (x)   81*\/  x     24*\2*|x|    + 9*\/  x  /    96*sign(x)                             \               \/ |x|               /|
                                         /       ___\ |  12*|x|      8*sign(x)   27*\/  x     4*\2*|x|    + 9*\/  x  / |   2*\x    - 3*x/*|- ---------- - ---------------- + ----------- + ---------- - -------------------------- + ---------- + ----------------------------------------------------------------|
                                      54*\-2 + \/ x /*|- --------- + --------- + ---------- - -------------------------|                  |       2           3 _____              4/3          2                               2      3 _____                           /              ____\                     |
             /                ____\                   |      x        3 _____        x            /              ____\ |                  |      x            \/ |x|            |x|            x            /              ____\     x*\/ |x|                            |   2/3       /  3 |                     |
             |     2/3       /  3 |                   |               \/ |x|                      |   2/3       /  3 | |                  |                                                               2 |   2/3       /  3 |                                       x*\|x|    + 2*\/  x  /                     |
   81    162*\2*|x|    + 9*\/  x  /                   \                                         x*\|x|    + 2*\/  x  / /                  \                                                              x *\|x|    + 2*\/  x  /                                                                                  /
- ---- - -------------------------- - ---------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
   3/2        /              ____\                                    /              ____\                                                                                                                    /              ____\                                                                                 
  x       3/2 |   2/3       /  3 |                                    |   2/3       /  3 |                                                                                                                    |   2/3       /  3 |                                                                                 
         x   *\|x|    + 2*\/  x  /                                  x*\|x|    + 2*\/  x  /                                                                                                                  x*\|x|    + 2*\/  x  /                                                                                 
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                  /              ____\                                                                                                                                             
                                                                                                                                                  |   2/3       /  3 |                                                                                                                                             
                                                                                                                                              216*\|x|    + 2*\/  x  /
−54(x−2)(8sign⁡(x)∣x∣3+27x3x−12∣x∣23x−4(9x3+2∣x∣23)2x(2x3+∣x∣23))x(2x3+∣x∣23)+2(x32−3x)(−96δ(x)∣x∣3+16sign⁡2(x)∣x∣43+96sign⁡(x)x∣x∣3+12(9x3+2∣x∣23)(8sign⁡(x)∣x∣3+27x3x−12∣x∣23x)x(2x3+∣x∣23)+81x3x2−144∣x∣23x2−24(9x3+2∣x∣23)3x2(2x3+∣x∣23)2)x(2x3+∣x∣23)−81x32−162(9x3+2∣x∣23)x32(2x3+∣x∣23)216(2x3+∣x∣23)\frac{- \frac{54 \left(\sqrt{x} - 2\right) \left(\frac{8 \operatorname{sign}{\left(x \right)}}{\sqrt[3]{\left|{x}\right|}} + \frac{27 \sqrt{x^{3}}}{x} - \frac{12 \left|{x}\right|^{\frac{2}{3}}}{x} - \frac{4 \left(9 \sqrt{x^{3}} + 2 \left|{x}\right|^{\frac{2}{3}}\right)^{2}}{x \left(2 \sqrt{x^{3}} + \left|{x}\right|^{\frac{2}{3}}\right)}\right)}{x \left(2 \sqrt{x^{3}} + \left|{x}\right|^{\frac{2}{3}}\right)} + \frac{2 \left(x^{\frac{3}{2}} - 3 x\right) \left(- \frac{96 \delta\left(x\right)}{\sqrt[3]{\left|{x}\right|}} + \frac{16 \operatorname{sign}^{2}{\left(x \right)}}{\left|{x}\right|^{\frac{4}{3}}} + \frac{96 \operatorname{sign}{\left(x \right)}}{x \sqrt[3]{\left|{x}\right|}} + \frac{12 \left(9 \sqrt{x^{3}} + 2 \left|{x}\right|^{\frac{2}{3}}\right) \left(\frac{8 \operatorname{sign}{\left(x \right)}}{\sqrt[3]{\left|{x}\right|}} + \frac{27 \sqrt{x^{3}}}{x} - \frac{12 \left|{x}\right|^{\frac{2}{3}}}{x}\right)}{x \left(2 \sqrt{x^{3}} + \left|{x}\right|^{\frac{2}{3}}\right)} + \frac{81 \sqrt{x^{3}}}{x^{2}} - \frac{144 \left|{x}\right|^{\frac{2}{3}}}{x^{2}} - \frac{24 \left(9 \sqrt{x^{3}} + 2 \left|{x}\right|^{\frac{2}{3}}\right)^{3}}{x^{2} \left(2 \sqrt{x^{3}} + \left|{x}\right|^{\frac{2}{3}}\right)^{2}}\right)}{x \left(2 \sqrt{x^{3}} + \left|{x}\right|^{\frac{2}{3}}\right)} - \frac{81}{x^{\frac{3}{2}}} - \frac{162 \left(9 \sqrt{x^{3}} + 2 \left|{x}\right|^{\frac{2}{3}}\right)}{x^{\frac{3}{2}} \left(2 \sqrt{x^{3}} + \left|{x}\right|^{\frac{2}{3}}\right)}}{216 \left(2 \sqrt{x^{3}} + \left|{x}\right|^{\frac{2}{3}}\right)}
Simplificar
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