Sr Examen

Otras calculadoras

y/((3*y^2+2)*3^y)

  • ¿Cómo usar?

  • Derivada de:
  • Derivada de (x^5+1) Derivada de (x^5+1)
  • Derivada de 8 Derivada de 8
  • Derivada de 7 Derivada de 7
  • Derivada de e^(2-x) Derivada de e^(2-x)

  • Expresiones idénticas

  • y/((tres *y^ dos + dos)* tres ^y)
  • y dividir por ((3 multiplicar por y al cuadrado más 2) multiplicar por 3 en el grado y)
  • y dividir por ((tres multiplicar por y en el grado dos más dos) multiplicar por tres en el grado y)
  • y/((3*y2+2)*3y)
  • y/3*y2+2*3y
  • y/((3*y²+2)*3^y)
  • y/((3*y en el grado 2+2)*3 en el grado y)
  • y/((3y^2+2)3^y)
  • y/((3y2+2)3y)
  • y/3y2+23y
  • y/3y^2+23^y
  • y dividir por ((3*y^2+2)*3^y)

  • Expresiones semejantes

  • y/((3*y^2-2)*3^y)
Derivada de la función/ 3*y^2/ y^2+2/ y/((3*y^2+2)*3^y)

Derivada de y/((3*y^2+2)*3^y)

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
      y      
-------------
/   2    \  y
\3*y  + 2/*3
y3y(3y2+2)\frac{y}{3^{y} \left(3 y^{2} + 2\right)} 
y/(((3*y^2 + 2)*3^y))
Solución detallada

  1. Se aplica la regla de la derivada parcial:

    ddyf(y)g(y)=−f(y)ddyg(y)+g(y)ddyf(y)g2(y)\frac{d}{d y} \frac{f{\left(y \right)}}{g{\left(y \right)}} = \frac{- f{\left(y \right)} \frac{d}{d y} g{\left(y \right)} + g{\left(y \right)} \frac{d}{d y} f{\left(y \right)}}{g^{2}{\left(y \right)}}

    f(y)=yf{\left(y \right)} = y y g(y)=3y(3y2+2)g{\left(y \right)} = 3^{y} \left(3 y^{2} + 2\right).

    Para calcular ddyf(y)\frac{d}{d y} f{\left(y \right)}:

    1. Según el principio, aplicamos: yy tenemos 11

    Para calcular ddyg(y)\frac{d}{d y} g{\left(y \right)}:

    1. Se aplica la regla de la derivada de una multiplicación:

      ddyf(y)g(y)=f(y)ddyg(y)+g(y)ddyf(y)\frac{d}{d y} f{\left(y \right)} g{\left(y \right)} = f{\left(y \right)} \frac{d}{d y} g{\left(y \right)} + g{\left(y \right)} \frac{d}{d y} f{\left(y \right)}

      f(y)=3yf{\left(y \right)} = 3^{y}; calculamos ddyf(y)\frac{d}{d y} f{\left(y \right)}:

      1. ddy3y=3ylog⁡(3)\frac{d}{d y} 3^{y} = 3^{y} \log{\left(3 \right)}

      g(y)=3y2+2g{\left(y \right)} = 3 y^{2} + 2; calculamos ddyg(y)\frac{d}{d y} g{\left(y \right)}:

      1. diferenciamos 3y2+23 y^{2} + 2 miembro por miembro:

        1. La derivada de una constante 22 es igual a cero.

        2. La derivada del producto de una constante por función es igual al producto de esta constante por la derivada de esta función.

          1. Según el principio, aplicamos: y2y^{2} tenemos 2y2 y

          Entonces, como resultado: 6y6 y

        Como resultado de: 6y6 y

      Como resultado de: 6⋅3yy+3y(3y2+2)log⁡(3)6 \cdot 3^{y} y + 3^{y} \left(3 y^{2} + 2\right) \log{\left(3 \right)}

    Ahora aplicamos la regla de la derivada de una divesión:

    3−2y(3y(3y2+2)−y(6⋅3yy+3y(3y2+2)log⁡(3)))(3y2+2)2\frac{3^{- 2 y} \left(3^{y} \left(3 y^{2} + 2\right) - y \left(6 \cdot 3^{y} y + 3^{y} \left(3 y^{2} + 2\right) \log{\left(3 \right)}\right)\right)}{\left(3 y^{2} + 2\right)^{2}}

  2. Simplificamos:

    3−y(3y2−y(6y+(3y2+2)log⁡(3))+2)(3y2+2)2\frac{3^{- y} \left(3 y^{2} - y \left(6 y + \left(3 y^{2} + 2\right) \log{\left(3 \right)}\right) + 2\right)}{\left(3 y^{2} + 2\right)^{2}}

Respuesta:

3−y(3y2−y(6y+(3y2+2)log⁡(3))+2)(3y2+2)2\frac{3^{- y} \left(3 y^{2} - y \left(6 y + \left(3 y^{2} + 2\right) \log{\left(3 \right)}\right) + 2\right)}{\left(3 y^{2} + 2\right)^{2}}

Gráfica
02468-8-6-4-2-1010-50005000
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
                   -2*y /       y    y /   2    \       \
      1         y*3    *\- 6*y*3  - 3 *\3*y  + 2/*log(3)/
------------- + -----------------------------------------
/   2    \  y                            2               
\3*y  + 2/*3                   /   2    \                
                               \3*y  + 2/
13y(3y2+2)+3−2yy(−6⋅3yy−3y(3y2+2)log⁡(3))(3y2+2)2\frac{1}{3^{y} \left(3 y^{2} + 2\right)} + \frac{3^{- 2 y} y \left(- 6 \cdot 3^{y} y - 3^{y} \left(3 y^{2} + 2\right) \log{\left(3 \right)}\right)}{\left(3 y^{2} + 2\right)^{2}}
Simplificar
Segunda derivada [src] 
    /          /                                                                                                                               /      /       2\       \\                      \
 -y |          |     /      /       2\       \ /  6*y            \   /      /       2\       \             2    /       2\                 6*y*\6*y + \2 + 3*y /*log(3)/|     /       2\       |
3  *|-12*y + y*|-6 + \6*y + \2 + 3*y /*log(3)/*|-------- + log(3)| + \6*y + \2 + 3*y /*log(3)/*log(3) - log (3)*\2 + 3*y / - 12*y*log(3) + -----------------------------| - 2*\2 + 3*y /*log(3)|
    |          |                               |       2         |                                                                                           2          |                      |
    \          \                               \2 + 3*y          /                                                                                    2 + 3*y           /                      /
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                    2                                                                                           
                                                                                          /       2\                                                                                            
                                                                                          \2 + 3*y /
3−y(y(6y(6y+(3y2+2)log⁡(3))3y2+2−12ylog⁡(3)+(6y+(3y2+2)log⁡(3))(6y3y2+2+log⁡(3))+(6y+(3y2+2)log⁡(3))log⁡(3)−(3y2+2)log⁡(3)2−6)−12y−2(3y2+2)log⁡(3))(3y2+2)2\frac{3^{- y} \left(y \left(\frac{6 y \left(6 y + \left(3 y^{2} + 2\right) \log{\left(3 \right)}\right)}{3 y^{2} + 2} - 12 y \log{\left(3 \right)} + \left(6 y + \left(3 y^{2} + 2\right) \log{\left(3 \right)}\right) \left(\frac{6 y}{3 y^{2} + 2} + \log{\left(3 \right)}\right) + \left(6 y + \left(3 y^{2} + 2\right) \log{\left(3 \right)}\right) \log{\left(3 \right)} - \left(3 y^{2} + 2\right) \log{\left(3 \right)}^{2} - 6\right) - 12 y - 2 \left(3 y^{2} + 2\right) \log{\left(3 \right)}\right)}{\left(3 y^{2} + 2\right)^{2}}
Simplificar
Tercera derivada [src] 
    /        /                                                                                                                                                                                                                                                                                                                                                                                                                                                             /      /       2\       \ /  6*y            \                                        \                                                                                                                                                             \
    |        |                                                                                                                                                                                                                                                                                                                                                                                                                                                         6*y*\6*y + \2 + 3*y /*log(3)/*|-------- + log(3)|                                        |                                                                                                                                                             |
    |        |                          /                            2                 \                                                                                                                   /      /       2\       \                                                                                                                                                       /       2    /       2\              \        2 /      /       2\       \                                 |       2         |        /      /       2\       \       |                                                                                                                                    /      /       2\       \|
 -y |        |/      /       2\       \ |   2         6          72*y       12*y*log(3)|   /        2    /       2\              \          /  6*y            \ /       2    /       2\              \   6*\6*y + \2 + 3*y /*log(3)/     /       2    /       2\              \               2    /      /       2\       \   /      /       2\       \ /  6*y            \          18*y*\6 + log (3)*\2 + 3*y / + 12*y*log(3)/   108*y *\6*y + \2 + 3*y /*log(3)/                                 \2 + 3*y          /   24*y*\6*y + \2 + 3*y /*log(3)/*log(3)|                      2    /       2\     /      /       2\       \ /  6*y            \     /      /       2\       \          18*y*\6*y + \2 + 3*y /*log(3)/|
3  *|-18 - y*|\6*y + \2 + 3*y /*log(3)/*|log (3) - -------- + ----------- + -----------| + \18 + log (3)*\2 + 3*y / + 18*y*log(3)/*log(3) - |-------- + log(3)|*\6 + log (3)*\2 + 3*y / + 12*y*log(3)/ - --------------------------- - 3*\6 + log (3)*\2 + 3*y / + 12*y*log(3)/*log(3) + 2*log (3)*\6*y + \2 + 3*y /*log(3)/ + \6*y + \2 + 3*y /*log(3)/*|-------- + log(3)|*log(3) - ------------------------------------------- + -------------------------------- + ------------------------------------------------- + -------------------------------------| - 36*y*log(3) - 3*log (3)*\2 + 3*y / + 3*\6*y + \2 + 3*y /*log(3)/*|-------- + log(3)| + 3*\6*y + \2 + 3*y /*log(3)/*log(3) + ------------------------------|
    |        |                          |                 2             2            2 |                                                    |       2         |                                                           2                                                                                                                              |       2         |                                   2                                        2                                          2                                             2              |                                                                    |       2         |                                                          2           |
    |        |                          |          2 + 3*y    /       2\      2 + 3*y  |                                                    \2 + 3*y          /                                                    2 + 3*y                                                                                                                               \2 + 3*y          /                            2 + 3*y                               /       2\                                    2 + 3*y                                       2 + 3*y               |                                                                    \2 + 3*y          /                                                   2 + 3*y            |
    \        \                          \                     \2 + 3*y /               /                                                                                                                                                                                                                                                                                                                                                      \2 + 3*y /                                                                                                        /                                                                                                                                                             /
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                                                                                                                                                                                                                                    2                                                                                                                                                                                                                                                                                                                                                          
                                                                                                                                                                                                                                                                                                                                                          /       2\                                                                                                                                                                                                                                                                                                                                                           
                                                                                                                                                                                                                                                                                                                                                          \2 + 3*y /
3−y(18y(6y+(3y2+2)log⁡(3))3y2+2−y(108y2(6y+(3y2+2)log⁡(3))(3y2+2)2+6y(6y+(3y2+2)log⁡(3))(6y3y2+2+log⁡(3))3y2+2+24y(6y+(3y2+2)log⁡(3))log⁡(3)3y2+2−18y(12ylog⁡(3)+(3y2+2)log⁡(3)2+6)3y2+2+(6y+(3y2+2)log⁡(3))(6y3y2+2+log⁡(3))log⁡(3)+(6y+(3y2+2)log⁡(3))(72y2(3y2+2)2+12ylog⁡(3)3y2+2+log⁡(3)2−63y2+2)+2(6y+(3y2+2)log⁡(3))log⁡(3)2−6(6y+(3y2+2)log⁡(3))3y2+2−(6y3y2+2+log⁡(3))(12ylog⁡(3)+(3y2+2)log⁡(3)2+6)−3(12ylog⁡(3)+(3y2+2)log⁡(3)2+6)log⁡(3)+(18ylog⁡(3)+(3y2+2)log⁡(3)2+18)log⁡(3))−36ylog⁡(3)+3(6y+(3y2+2)log⁡(3))(6y3y2+2+log⁡(3))+3(6y+(3y2+2)log⁡(3))log⁡(3)−3(3y2+2)log⁡(3)2−18)(3y2+2)2\frac{3^{- y} \left(\frac{18 y \left(6 y + \left(3 y^{2} + 2\right) \log{\left(3 \right)}\right)}{3 y^{2} + 2} - y \left(\frac{108 y^{2} \left(6 y + \left(3 y^{2} + 2\right) \log{\left(3 \right)}\right)}{\left(3 y^{2} + 2\right)^{2}} + \frac{6 y \left(6 y + \left(3 y^{2} + 2\right) \log{\left(3 \right)}\right) \left(\frac{6 y}{3 y^{2} + 2} + \log{\left(3 \right)}\right)}{3 y^{2} + 2} + \frac{24 y \left(6 y + \left(3 y^{2} + 2\right) \log{\left(3 \right)}\right) \log{\left(3 \right)}}{3 y^{2} + 2} - \frac{18 y \left(12 y \log{\left(3 \right)} + \left(3 y^{2} + 2\right) \log{\left(3 \right)}^{2} + 6\right)}{3 y^{2} + 2} + \left(6 y + \left(3 y^{2} + 2\right) \log{\left(3 \right)}\right) \left(\frac{6 y}{3 y^{2} + 2} + \log{\left(3 \right)}\right) \log{\left(3 \right)} + \left(6 y + \left(3 y^{2} + 2\right) \log{\left(3 \right)}\right) \left(\frac{72 y^{2}}{\left(3 y^{2} + 2\right)^{2}} + \frac{12 y \log{\left(3 \right)}}{3 y^{2} + 2} + \log{\left(3 \right)}^{2} - \frac{6}{3 y^{2} + 2}\right) + 2 \left(6 y + \left(3 y^{2} + 2\right) \log{\left(3 \right)}\right) \log{\left(3 \right)}^{2} - \frac{6 \left(6 y + \left(3 y^{2} + 2\right) \log{\left(3 \right)}\right)}{3 y^{2} + 2} - \left(\frac{6 y}{3 y^{2} + 2} + \log{\left(3 \right)}\right) \left(12 y \log{\left(3 \right)} + \left(3 y^{2} + 2\right) \log{\left(3 \right)}^{2} + 6\right) - 3 \left(12 y \log{\left(3 \right)} + \left(3 y^{2} + 2\right) \log{\left(3 \right)}^{2} + 6\right) \log{\left(3 \right)} + \left(18 y \log{\left(3 \right)} + \left(3 y^{2} + 2\right) \log{\left(3 \right)}^{2} + 18\right) \log{\left(3 \right)}\right) - 36 y \log{\left(3 \right)} + 3 \left(6 y + \left(3 y^{2} + 2\right) \log{\left(3 \right)}\right) \left(\frac{6 y}{3 y^{2} + 2} + \log{\left(3 \right)}\right) + 3 \left(6 y + \left(3 y^{2} + 2\right) \log{\left(3 \right)}\right) \log{\left(3 \right)} - 3 \left(3 y^{2} + 2\right) \log{\left(3 \right)}^{2} - 18\right)}{\left(3 y^{2} + 2\right)^{2}}
Simplificar
Gráfico
Derivada de y/((3*y^2+2)*3^y)
    © Sr Examen – Калькулятор