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  • Derivada de x^-4/5 Derivada de x^-4/5
  • Derivada de x^2*5^x Derivada de x^2*5^x
  • Derivada de x/(1+e^x) Derivada de x/(1+e^x)
  • Derivada de u/v

  • Expresiones idénticas

  • (seis *(seis *(x- tres)^ dos)^(uno / tres))/((x- uno)^ dos + ocho)
  • (6 multiplicar por (6 multiplicar por (x menos 3) al cuadrado ) en el grado (1 dividir por 3)) dividir por ((x menos 1) al cuadrado más 8)
  • (seis multiplicar por (seis multiplicar por (x menos tres) en el grado dos) en el grado (uno dividir por tres)) dividir por ((x menos uno) en el grado dos más ocho)
  • (6*(6*(x-3)2)(1/3))/((x-1)2+8)
  • 6*6*x-321/3/x-12+8
  • (6*(6*(x-3)²)^(1/3))/((x-1)²+8)
  • (6*(6*(x-3) en el grado 2) en el grado (1/3))/((x-1) en el grado 2+8)
  • (6(6(x-3)^2)^(1/3))/((x-1)^2+8)
  • (6(6(x-3)2)(1/3))/((x-1)2+8)
  • 66x-321/3/x-12+8
  • 66x-3^2^1/3/x-1^2+8
  • (6*(6*(x-3)^2)^(1 dividir por 3)) dividir por ((x-1)^2+8)

  • Expresiones semejantes

  • (6*(6*(x-3)^2)^(1/3))/((x-1)^2-8)
  • (6*(6*(x-3)^2)^(1/3))/((x+1)^2+8)
  • (6*(6*(x+3)^2)^(1/3))/((x-1)^2+8)
Derivada de la función/ (6*(6*(x-3)^2)^(1/3))/((x-1)^2+8)

Derivada de (6*(6*(x-3)^2)^(1/3))/((x-1)^2+8)

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
     ____________
  3 /          2 
6*\/  6*(x - 3)  
-----------------
          2      
   (x - 1)  + 8
66(x−3)23(x−1)2+8\frac{6 \sqrt[3]{6 \left(x - 3\right)^{2}}}{\left(x - 1\right)^{2} + 8} 
(6*(6*(x - 3)^2)^(1/3))/((x - 1)^2 + 8)
Primera derivada [src] 
  3 ___        2/3             3 ___        2/3            
6*\/ 6 *|x - 3|   *(2 - 2*x)   \/ 6 *|x - 3|   *(-12 + 4*x)
---------------------------- + ----------------------------
                    2                   2 /       2    \   
      /       2    \             (x - 3) *\(x - 1)  + 8/   
      \(x - 1)  + 8/
663∣x−3∣23(2−2x)((x−1)2+8)2+63(4x−12)∣x−3∣23(x−3)2((x−1)2+8)\frac{6 \sqrt[3]{6} \left|{x - 3}\right|^{\frac{2}{3}} \left(2 - 2 x\right)}{\left(\left(x - 1\right)^{2} + 8\right)^{2}} + \frac{\sqrt[3]{6} \left(4 x - 12\right) \left|{x - 3}\right|^{\frac{2}{3}}}{\left(x - 3\right)^{2} \left(\left(x - 1\right)^{2} + 8\right)}
Simplificar
Segunda derivada [src] 
        /            2/3                                  /                2 \                           \
        |  3*|-3 + x|      2*sign(-3 + x)             2/3 |      4*(-1 + x)  |                           |
        |- ------------- + --------------   3*|-3 + x|   *|-1 + -------------|                           |
        |      -3 + x       3 __________                  |                 2|              2/3          |
  3 ___ |                   \/ |-3 + x|                   \     8 + (-1 + x) /    4*|-3 + x|   *(-1 + x) |
4*\/ 6 *|-------------------------------- + ---------------------------------- - ------------------------|
        |           3*(-3 + x)                                    2                       /            2\|
        \                                             8 + (-1 + x)               (-3 + x)*\8 + (-1 + x) //
----------------------------------------------------------------------------------------------------------
                                                          2                                               
                                              8 + (-1 + x)
463(3(4(x−1)2(x−1)2+8−1)∣x−3∣23(x−1)2+8−4(x−1)∣x−3∣23(x−3)((x−1)2+8)+2sign⁡(x−3)∣x−3∣3−3∣x−3∣23x−33(x−3))(x−1)2+8\frac{4 \sqrt[3]{6} \left(\frac{3 \left(\frac{4 \left(x - 1\right)^{2}}{\left(x - 1\right)^{2} + 8} - 1\right) \left|{x - 3}\right|^{\frac{2}{3}}}{\left(x - 1\right)^{2} + 8} - \frac{4 \left(x - 1\right) \left|{x - 3}\right|^{\frac{2}{3}}}{\left(x - 3\right) \left(\left(x - 1\right)^{2} + 8\right)} + \frac{\frac{2 \operatorname{sign}{\left(x - 3 \right)}}{\sqrt[3]{\left|{x - 3}\right|}} - \frac{3 \left|{x - 3}\right|^{\frac{2}{3}}}{x - 3}}{3 \left(x - 3\right)}\right)}{\left(x - 1\right)^{2} + 8}
Simplificar
Tercera derivada [src] 
        /      2                                            2/3                                    /            2/3                 \                           /                2 \                 /                2 \\
        |  sign (-3 + x)   6*DiracDelta(-3 + x)   9*|-3 + x|          6*sign(-3 + x)               |  3*|-3 + x|      2*sign(-3 + x)|              2/3          |      2*(-1 + x)  |             2/3 |      4*(-1 + x)  ||
        |- ------------- + -------------------- + ------------- - ---------------------   (-1 + x)*|- ------------- + --------------|   18*|-3 + x|   *(-1 + x)*|-1 + -------------|   3*|-3 + x|   *|-1 + -------------||
        |           4/3        3 __________                 2              3 __________            |      -3 + x       3 __________ |                           |                 2|                 |                 2||
  3 ___ |   |-3 + x|           \/ |-3 + x|          (-3 + x)      (-3 + x)*\/ |-3 + x|             \                   \/ |-3 + x|  /                           \     8 + (-1 + x) /                 \     8 + (-1 + x) /|
8*\/ 6 *|------------------------------------------------------------------------------ - ------------------------------------------- - -------------------------------------------- + ----------------------------------|
        |                                  9*(-3 + x)                                                        /            2\                                         2                               /            2\     |
        |                                                                                           (-3 + x)*\8 + (-1 + x) /                          /            2\                       (-3 + x)*\8 + (-1 + x) /     |
        \                                                                                                                                             \8 + (-1 + x) /                                                    /
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                  2                                                                                                       
                                                                                                      8 + (-1 + x)
863(−18(x−1)(2(x−1)2(x−1)2+8−1)∣x−3∣23((x−1)2+8)2−(x−1)(2sign⁡(x−3)∣x−3∣3−3∣x−3∣23x−3)(x−3)((x−1)2+8)+3(4(x−1)2(x−1)2+8−1)∣x−3∣23(x−3)((x−1)2+8)+6δ(x−3)∣x−3∣3−sign⁡2(x−3)∣x−3∣43−6sign⁡(x−3)(x−3)∣x−3∣3+9∣x−3∣23(x−3)29(x−3))(x−1)2+8\frac{8 \sqrt[3]{6} \left(- \frac{18 \left(x - 1\right) \left(\frac{2 \left(x - 1\right)^{2}}{\left(x - 1\right)^{2} + 8} - 1\right) \left|{x - 3}\right|^{\frac{2}{3}}}{\left(\left(x - 1\right)^{2} + 8\right)^{2}} - \frac{\left(x - 1\right) \left(\frac{2 \operatorname{sign}{\left(x - 3 \right)}}{\sqrt[3]{\left|{x - 3}\right|}} - \frac{3 \left|{x - 3}\right|^{\frac{2}{3}}}{x - 3}\right)}{\left(x - 3\right) \left(\left(x - 1\right)^{2} + 8\right)} + \frac{3 \left(\frac{4 \left(x - 1\right)^{2}}{\left(x - 1\right)^{2} + 8} - 1\right) \left|{x - 3}\right|^{\frac{2}{3}}}{\left(x - 3\right) \left(\left(x - 1\right)^{2} + 8\right)} + \frac{\frac{6 \delta\left(x - 3\right)}{\sqrt[3]{\left|{x - 3}\right|}} - \frac{\operatorname{sign}^{2}{\left(x - 3 \right)}}{\left|{x - 3}\right|^{\frac{4}{3}}} - \frac{6 \operatorname{sign}{\left(x - 3 \right)}}{\left(x - 3\right) \sqrt[3]{\left|{x - 3}\right|}} + \frac{9 \left|{x - 3}\right|^{\frac{2}{3}}}{\left(x - 3\right)^{2}}}{9 \left(x - 3\right)}\right)}{\left(x - 1\right)^{2} + 8}
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