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y=(e^(-15x*sinx^3))/((cos^3)lg*x^2)

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  • Derivada de:
  • Derivada de 7^(3*x-1) Derivada de 7^(3*x-1)
  • Derivada de 6^(x^2-8x+28) Derivada de 6^(x^2-8x+28)
  • Derivada de -5*tan(2*t)-4*cot(4*t) Derivada de -5*tan(2*t)-4*cot(4*t)
  • Derivada de 5(3-2x)^2 Derivada de 5(3-2x)^2

  • Expresiones idénticas

  • y=(e^(-15x*sinx^ tres))/((cos^ tres)lg*x^ dos)
  • y es igual a (e en el grado ( menos 15x multiplicar por seno de x al cubo )) dividir por (( coseno de al cubo )lg multiplicar por x al cuadrado )
  • y es igual a (e en el grado ( menos 15x multiplicar por seno de x en el grado tres)) dividir por (( coseno de en el grado tres)lg multiplicar por x en el grado dos)
  • y=(e(-15x*sinx3))/((cos3)lg*x2)
  • y=e-15x*sinx3/cos3lg*x2
  • y=(e^(-15x*sinx³))/((cos³)lg*x²)
  • y=(e en el grado (-15x*sinx en el grado 3))/((cos en el grado 3)lg*x en el grado 2)
  • y=(e^(-15xsinx^3))/((cos^3)lgx^2)
  • y=(e(-15xsinx3))/((cos3)lgx2)
  • y=e-15xsinx3/cos3lgx2
  • y=e^-15xsinx^3/cos^3lgx^2
  • y=(e^(-15x*sinx^3)) dividir por ((cos^3)lg*x^2)

  • Expresiones semejantes

  • y=(e^(15x*sinx^3))/((cos^3)lg*x^2)
Derivada de la función/ y=(e^(-15x*sinx^3))/((cos^3)lg*x^2)

Derivada de y=(e^(-15x*sinx^3))/((cos^3)lg*x^2)

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
           3   
  -15*x*sin (x)
 E             
---------------
   3       2   
cos (x)*log (x)
e−15xsin⁡3(x)log⁡(x)2cos⁡3(x)\frac{e^{- 15 x \sin^{3}{\left(x \right)}}}{\log{\left(x \right)}^{2} \cos^{3}{\left(x \right)}} 
E^((-15*x)*sin(x)^3)/((cos(x)^3*log(x)^2))
Solución detallada

  1. Se aplica la regla de la derivada parcial:

    ddxf(x)g(x)=−f(x)ddxg(x)+g(x)ddxf(x)g2(x)\frac{d}{d x} \frac{f{\left(x \right)}}{g{\left(x \right)}} = \frac{- f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}}{g^{2}{\left(x \right)}}

    f(x)=e−15xsin⁡3(x)f{\left(x \right)} = e^{- 15 x \sin^{3}{\left(x \right)}} y g(x)=log⁡(x)2cos⁡3(x)g{\left(x \right)} = \log{\left(x \right)}^{2} \cos^{3}{\left(x \right)}.

    Para calcular ddxf(x)\frac{d}{d x} f{\left(x \right)}:

    1. Sustituimos u=−15xsin⁡3(x)u = - 15 x \sin^{3}{\left(x \right)}.

    2. Derivado eue^{u} es.

    3. Luego se aplica una cadena de reglas. Multiplicamos por ddx−15xsin⁡3(x)\frac{d}{d x} - 15 x \sin^{3}{\left(x \right)}:

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

        ddxf(x)g(x)=f(x)ddxg(x)+g(x)ddxf(x)\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}

        f(x)=−15xf{\left(x \right)} = - 15 x; calculamos ddxf(x)\frac{d}{d x} f{\left(x \right)}:

        1. 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: xx tenemos 11

          Entonces, como resultado: −15-15

        g(x)=sin⁡3(x)g{\left(x \right)} = \sin^{3}{\left(x \right)}; calculamos ddxg(x)\frac{d}{d x} g{\left(x \right)}:

        1. Sustituimos u=sin⁡(x)u = \sin{\left(x \right)}.

        2. Según el principio, aplicamos: u3u^{3} tenemos 3u23 u^{2}

        3. Luego se aplica una cadena de reglas. Multiplicamos por ddxsin⁡(x)\frac{d}{d x} \sin{\left(x \right)}:

          1. La derivada del seno es igual al coseno:

            ddxsin⁡(x)=cos⁡(x)\frac{d}{d x} \sin{\left(x \right)} = \cos{\left(x \right)}

          Como resultado de la secuencia de reglas:

          3sin⁡2(x)cos⁡(x)3 \sin^{2}{\left(x \right)} \cos{\left(x \right)}

        Como resultado de: −45xsin⁡2(x)cos⁡(x)−15sin⁡3(x)- 45 x \sin^{2}{\left(x \right)} \cos{\left(x \right)} - 15 \sin^{3}{\left(x \right)}

      Como resultado de la secuencia de reglas:

      (−45xsin⁡2(x)cos⁡(x)−15sin⁡3(x))e−15xsin⁡3(x)\left(- 45 x \sin^{2}{\left(x \right)} \cos{\left(x \right)} - 15 \sin^{3}{\left(x \right)}\right) e^{- 15 x \sin^{3}{\left(x \right)}}

    Para calcular ddxg(x)\frac{d}{d x} g{\left(x \right)}:

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

      ddxf(x)g(x)=f(x)ddxg(x)+g(x)ddxf(x)\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}

      f(x)=cos⁡3(x)f{\left(x \right)} = \cos^{3}{\left(x \right)}; calculamos ddxf(x)\frac{d}{d x} f{\left(x \right)}:

      1. Sustituimos u=cos⁡(x)u = \cos{\left(x \right)}.

      2. Según el principio, aplicamos: u3u^{3} tenemos 3u23 u^{2}

      3. Luego se aplica una cadena de reglas. Multiplicamos por ddxcos⁡(x)\frac{d}{d x} \cos{\left(x \right)}:

        1. La derivada del coseno es igual a menos el seno:

          ddxcos⁡(x)=−sin⁡(x)\frac{d}{d x} \cos{\left(x \right)} = - \sin{\left(x \right)}

        Como resultado de la secuencia de reglas:

        −3sin⁡(x)cos⁡2(x)- 3 \sin{\left(x \right)} \cos^{2}{\left(x \right)}

      g(x)=log⁡(x)2g{\left(x \right)} = \log{\left(x \right)}^{2}; calculamos ddxg(x)\frac{d}{d x} g{\left(x \right)}:

      1. Sustituimos u=log⁡(x)u = \log{\left(x \right)}.

      2. Según el principio, aplicamos: u2u^{2} tenemos 2u2 u

      3. Luego se aplica una cadena de reglas. Multiplicamos por ddxlog⁡(x)\frac{d}{d x} \log{\left(x \right)}:

        1. Derivado log⁡(x)\log{\left(x \right)} es 1x\frac{1}{x}.

        Como resultado de la secuencia de reglas:

        2log⁡(x)x\frac{2 \log{\left(x \right)}}{x}

      Como resultado de: −3log⁡(x)2sin⁡(x)cos⁡2(x)+2log⁡(x)cos⁡3(x)x- 3 \log{\left(x \right)}^{2} \sin{\left(x \right)} \cos^{2}{\left(x \right)} + \frac{2 \log{\left(x \right)} \cos^{3}{\left(x \right)}}{x}

    Ahora aplicamos la regla de la derivada de una divesión:

    (−45xsin⁡2(x)cos⁡(x)−15sin⁡3(x))e−15xsin⁡3(x)log⁡(x)2cos⁡3(x)−(−3log⁡(x)2sin⁡(x)cos⁡2(x)+2log⁡(x)cos⁡3(x)x)e−15xsin⁡3(x)log⁡(x)4cos⁡6(x)\frac{\left(- 45 x \sin^{2}{\left(x \right)} \cos{\left(x \right)} - 15 \sin^{3}{\left(x \right)}\right) e^{- 15 x \sin^{3}{\left(x \right)}} \log{\left(x \right)}^{2} \cos^{3}{\left(x \right)} - \left(- 3 \log{\left(x \right)}^{2} \sin{\left(x \right)} \cos^{2}{\left(x \right)} + \frac{2 \log{\left(x \right)} \cos^{3}{\left(x \right)}}{x}\right) e^{- 15 x \sin^{3}{\left(x \right)}}}{\log{\left(x \right)}^{4} \cos^{6}{\left(x \right)}}

  2. Simplificamos:

    (−15x(3xcos⁡(x)+sin⁡(x))log⁡(x)sin⁡2(x)cos⁡(x)+3xlog⁡(x)sin⁡(x)−2cos⁡(x))e−15xsin⁡3(x)xlog⁡(x)3cos⁡4(x)\frac{\left(- 15 x \left(3 x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x \right)} \sin^{2}{\left(x \right)} \cos{\left(x \right)} + 3 x \log{\left(x \right)} \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) e^{- 15 x \sin^{3}{\left(x \right)}}}{x \log{\left(x \right)}^{3} \cos^{4}{\left(x \right)}}

Respuesta:

(−15x(3xcos⁡(x)+sin⁡(x))log⁡(x)sin⁡2(x)cos⁡(x)+3xlog⁡(x)sin⁡(x)−2cos⁡(x))e−15xsin⁡3(x)xlog⁡(x)3cos⁡4(x)\frac{\left(- 15 x \left(3 x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x \right)} \sin^{2}{\left(x \right)} \cos{\left(x \right)} + 3 x \log{\left(x \right)} \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) e^{- 15 x \sin^{3}{\left(x \right)}}}{x \log{\left(x \right)}^{3} \cos^{4}{\left(x \right)}}

Gráfica
02468-8-6-4-2-1010-1e375e36
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
                                                                      /       3                                     \           3   
                                                                      |  2*cos (x)*log(x)        2       2          |  -15*x*sin (x)
                                                               3      |- ---------------- + 3*cos (x)*log (x)*sin(x)|*e             
       1        /        3              2          \  -15*x*sin (x)   \         x                                   /               
---------------*\- 15*sin (x) - 45*x*sin (x)*cos(x)/*e              + --------------------------------------------------------------
   3       2                                                                                    6       4                           
cos (x)*log (x)                                                                              cos (x)*log (x)
1log⁡(x)2cos⁡3(x)(−45xsin⁡2(x)cos⁡(x)−15sin⁡3(x))e−15xsin⁡3(x)+(3log⁡(x)2sin⁡(x)cos⁡2(x)−2log⁡(x)cos⁡3(x)x)e−15xsin⁡3(x)log⁡(x)4cos⁡6(x)\frac{1}{\log{\left(x \right)}^{2} \cos^{3}{\left(x \right)}} \left(- 45 x \sin^{2}{\left(x \right)} \cos{\left(x \right)} - 15 \sin^{3}{\left(x \right)}\right) e^{- 15 x \sin^{3}{\left(x \right)}} + \frac{\left(3 \log{\left(x \right)}^{2} \sin{\left(x \right)} \cos^{2}{\left(x \right)} - \frac{2 \log{\left(x \right)} \cos^{3}{\left(x \right)}}{x}\right) e^{- 15 x \sin^{3}{\left(x \right)}}}{\log{\left(x \right)}^{4} \cos^{6}{\left(x \right)}}
Simplificar
Segunda derivada [src] 
/                                                                                                                                                                               2                               2                                                                                                                                                                                   \               
|                                                                                                                                                           2       2      2*cos (x)        2       2      2*cos (x)*log(x)   12*cos(x)*log(x)*sin(x)                                                                                                                                               |               
|                                                                                                                                                    - 6*log (x)*sin (x) - --------- + 3*cos (x)*log (x) + ---------------- + -----------------------     /  2*cos(x)                  \     /  2*cos(x)                  \                                                                         |               
|                                                                                                                                                                               2                                  2                     x              2*|- -------- + 3*log(x)*sin(x)|   3*|- -------- + 3*log(x)*sin(x)|*sin(x)                                                                  |               
|                                                                                           /     2       3*sin(x)\ /  2*cos(x)                  \                             x                                  x                                       \     x                      /     \     x                      /                2    /  2*cos(x)                  \                      |               
|                                                                                           |- -------- + --------|*|- -------- + 3*log(x)*sin(x)| + ------------------------------------------------------------------------------------------------ - -------------------------------- + ---------------------------------------   30*sin (x)*|- -------- + 3*log(x)*sin(x)|*(3*x*cos(x) + sin(x))|           3   
|   /     2             2                                               2    3   \          \  x*log(x)    cos(x) / \     x                      /                                            cos(x)*log(x)                                                         x*log(x)                                cos(x)                              \     x                      /                      |  -15*x*sin (x)
|45*\x*sin (x) - 2*x*cos (x) - 2*cos(x)*sin(x) + 5*(3*x*cos(x) + sin(x)) *sin (x)/*sin(x) + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------|*e             
\                                                                                                                                                                                                       cos(x)*log(x)                                                                                                                                         cos(x)*log(x)                         /               
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                                                                     3       2                                                                                                                                                                                                      
                                                                                                                                                                                                  cos (x)*log (x)
(−30(3xcos⁡(x)+sin⁡(x))(3log⁡(x)sin⁡(x)−2cos⁡(x)x)sin⁡2(x)log⁡(x)cos⁡(x)+45(xsin⁡2(x)−2xcos⁡2(x)+5(3xcos⁡(x)+sin⁡(x))2sin⁡3(x)−2sin⁡(x)cos⁡(x))sin⁡(x)+(3log⁡(x)sin⁡(x)−2cos⁡(x)x)(3sin⁡(x)cos⁡(x)−2xlog⁡(x))+3(3log⁡(x)sin⁡(x)−2cos⁡(x)x)sin⁡(x)cos⁡(x)+−6log⁡(x)2sin⁡2(x)+3log⁡(x)2cos⁡2(x)+12log⁡(x)sin⁡(x)cos⁡(x)x+2log⁡(x)cos⁡2(x)x2−2cos⁡2(x)x2log⁡(x)cos⁡(x)−2(3log⁡(x)sin⁡(x)−2cos⁡(x)x)xlog⁡(x)log⁡(x)cos⁡(x))e−15xsin⁡3(x)log⁡(x)2cos⁡3(x)\frac{\left(- \frac{30 \left(3 x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \left(3 \log{\left(x \right)} \sin{\left(x \right)} - \frac{2 \cos{\left(x \right)}}{x}\right) \sin^{2}{\left(x \right)}}{\log{\left(x \right)} \cos{\left(x \right)}} + 45 \left(x \sin^{2}{\left(x \right)} - 2 x \cos^{2}{\left(x \right)} + 5 \left(3 x \cos{\left(x \right)} + \sin{\left(x \right)}\right)^{2} \sin^{3}{\left(x \right)} - 2 \sin{\left(x \right)} \cos{\left(x \right)}\right) \sin{\left(x \right)} + \frac{\left(3 \log{\left(x \right)} \sin{\left(x \right)} - \frac{2 \cos{\left(x \right)}}{x}\right) \left(\frac{3 \sin{\left(x \right)}}{\cos{\left(x \right)}} - \frac{2}{x \log{\left(x \right)}}\right) + \frac{3 \left(3 \log{\left(x \right)} \sin{\left(x \right)} - \frac{2 \cos{\left(x \right)}}{x}\right) \sin{\left(x \right)}}{\cos{\left(x \right)}} + \frac{- 6 \log{\left(x \right)}^{2} \sin^{2}{\left(x \right)} + 3 \log{\left(x \right)}^{2} \cos^{2}{\left(x \right)} + \frac{12 \log{\left(x \right)} \sin{\left(x \right)} \cos{\left(x \right)}}{x} + \frac{2 \log{\left(x \right)} \cos^{2}{\left(x \right)}}{x^{2}} - \frac{2 \cos^{2}{\left(x \right)}}{x^{2}}}{\log{\left(x \right)} \cos{\left(x \right)}} - \frac{2 \left(3 \log{\left(x \right)} \sin{\left(x \right)} - \frac{2 \cos{\left(x \right)}}{x}\right)}{x \log{\left(x \right)}}}{\log{\left(x \right)} \cos{\left(x \right)}}\right) e^{- 15 x \sin^{3}{\left(x \right)}}}{\log{\left(x \right)}^{2} \cos^{3}{\left(x \right)}}
Simplificar
Tercera derivada [src] 
/                                                                                                                                                                                                                       3                                                           3                   3                   2                   2                          2                                                                                                                                                               /                           2                               2                                    \     /                           2                               2                                    \                                                                                                                                  /                           2                               2                                    \                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   \               
|                                                                                                                                                                                                                  6*cos (x)        2       3            2       2             4*cos (x)*log(x)   18*cos (x)*log(x)   18*cos (x)*sin(x)   36*sin (x)*cos(x)*log(x)   18*cos (x)*log(x)*sin(x)                                                                                                                      /     2       3*sin(x)\ |       2       2      2*cos (x)        2       2      2*cos (x)*log(x)   12*cos(x)*log(x)*sin(x)|     |       2       2      2*cos (x)        2       2      2*cos (x)*log(x)   12*cos(x)*log(x)*sin(x)|                                                                                                                                  |       2       2      2*cos (x)        2       2      2*cos (x)*log(x)   12*cos(x)*log(x)*sin(x)|                                                                                                                                                                                                /                                                                                    2                               2                                                                                                                 \                                                                                                                           |               
|                                                                                                                                                                                                                  --------- + 6*log (x)*sin (x) - 21*cos (x)*log (x)*sin(x) - ---------------- + ----------------- + ----------------- - ------------------------ - ------------------------     /  2*cos(x)                  \      /  2*cos(x)                  \         2    /  2*cos(x)                  \   |- -------- + --------|*|- 6*log (x)*sin (x) - --------- + 3*cos (x)*log (x) + ---------------- + -----------------------|   6*|- 6*log (x)*sin (x) - --------- + 3*cos (x)*log (x) + ---------------- + -----------------------|     /     2       3*sin(x)\ /  2*cos(x)                  \     /     2       3*sin(x)\ /  2*cos(x)                  \          9*|- 6*log (x)*sin (x) - --------- + 3*cos (x)*log (x) + ---------------- + -----------------------|*sin(x)      /  2*cos(x)                  \                                                                                                                                                     |                                                                2       2      2*cos (x)        2       2      2*cos (x)*log(x)   12*cos(x)*log(x)*sin(x)                                                                             |                                                                                                                           |               
|                                                                                                                       /                                   2                     \                                     3                                                              3                  x                    2                     x                           2              2*|- -------- + 3*log(x)*sin(x)|   10*|- -------- + 3*log(x)*sin(x)|   21*sin (x)*|- -------- + 3*log(x)*sin(x)|   \  x*log(x)    cos(x) / |                           2                                  2                     x           |     |                           2                                  2                     x           |   2*|- -------- + --------|*|- -------- + 3*log(x)*sin(x)|   3*|- -------- + --------|*|- -------- + 3*log(x)*sin(x)|*sin(x)     |                           2                                  2                     x           |          24*|- -------- + 3*log(x)*sin(x)|*sin(x)                                                                                                                                              |                                                         - 6*log (x)*sin (x) - --------- + 3*cos (x)*log (x) + ---------------- + -----------------------     /  2*cos(x)                  \     /  2*cos(x)                  \       |                                                                                                                           |               
|                                                                                        /  2*cos(x)                  \ |        2           6        12*sin (x)      12*sin(x)   |   6*cos(x)                         x                                                              x                                       x                                                 x                 \     x                      /      \     x                      /              \     x                      /                           \                          x                                  x                                  /     \                          x                                  x                                  /     \  x*log(x)    cos(x) / \     x                      /     \  x*log(x)    cos(x) / \     x                      /            \                          x                                  x                                  /             \     x                      /                                                                                                                                                     |                                                                                    2                                  2                     x              2*|- -------- + 3*log(x)*sin(x)|   3*|- -------- + 3*log(x)*sin(x)|*sin(x)|                                                                                                                           |               
|                                                                                        |- -------- + 3*log(x)*sin(x)|*|3 + --------- + ---------- + ---------- - ---------------| - -------- + 9*log(x)*sin(x) + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------- + --------------------------------- + ----------------------------------------- + -------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------- - -------------------------------------------------------- + --------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------- - ----------------------------------------                                                                                                                   2                          |/     2       3*sin(x)\ /  2*cos(x)                  \                             x                                  x                                       \     x                      /     \     x                      /       |       /  2*cos(x)                  \ /     2             2                                               2    3   \       |               
|                                                                                        \     x                      / |     2           2    2          2        x*cos(x)*log(x)|      x                                                                                                          2                                                                                                       2                                   2    2                                     2                                                                             cos(x)*log(x)                                                                                                                2                                                                        x*log(x)                                                        cos(x)                                                                                 2                                                                       x*cos(x)*log(x)                                                                                                                          45*sin (x)*(3*x*cos(x) + sin(x))*||- -------- + --------|*|- -------- + 3*log(x)*sin(x)| + ------------------------------------------------------------------------------------------------ - -------------------------------- + ---------------------------------------|   135*|- -------- + 3*log(x)*sin(x)|*\x*sin (x) - 2*x*cos (x) - 2*cos(x)*sin(x) + 5*(3*x*cos(x) + sin(x)) *sin (x)/*sin(x)|           3   
|       3                                3    6             2                     3                                     \    x *log(x)   x *log (x)    cos (x)                    /                                                                                                              cos (x)*log(x)                                                                                            x *log(x)                           x *log (x)                               cos (x)                                                                                                                                                                                           x*cos(x)*log (x)                                                                                                                                                                                                                         cos (x)*log(x)                                                                                                     2                     3                          /       2             2                     \                                    \\  x*log(x)    cos(x) / \     x                      /                                            cos(x)*log(x)                                                         x*log(x)                                cos(x)                /       \     x                      /                                                                                      |  -15*x*sin (x)
|135*sin (x) - 3375*(3*x*cos(x) + sin(x)) *sin (x) - 270*cos (x)*sin(x) - 90*x*cos (x) + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + 315*x*sin (x)*cos(x) + 2025*sin (x)*(3*x*cos(x) + sin(x))*\- x*sin (x) + 2*x*cos (x) + 2*cos(x)*sin(x)/ - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------|*e             
\                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          cos(x)*log(x)                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             cos(x)*log(x)                                                                                                                                                                                      cos(x)*log(x)                                                      /               
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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              cos (x)*log (x)
(315xsin⁡2(x)cos⁡(x)−90xcos⁡3(x)−3375(3xcos⁡(x)+sin⁡(x))3sin⁡6(x)+2025(3xcos⁡(x)+sin⁡(x))(−xsin⁡2(x)+2xcos⁡2(x)+2sin⁡(x)cos⁡(x))sin⁡3(x)−45(3xcos⁡(x)+sin⁡(x))((3log⁡(x)sin⁡(x)−2cos⁡(x)x)(3sin⁡(x)cos⁡(x)−2xlog⁡(x))+3(3log⁡(x)sin⁡(x)−2cos⁡(x)x)sin⁡(x)cos⁡(x)+−6log⁡(x)2sin⁡2(x)+3log⁡(x)2cos⁡2(x)+12log⁡(x)sin⁡(x)cos⁡(x)x+2log⁡(x)cos⁡2(x)x2−2cos⁡2(x)x2log⁡(x)cos⁡(x)−2(3log⁡(x)sin⁡(x)−2cos⁡(x)x)xlog⁡(x))sin⁡2(x)log⁡(x)cos⁡(x)+135(3log⁡(x)sin⁡(x)−2cos⁡(x)x)(xsin⁡2(x)−2xcos⁡2(x)+5(3xcos⁡(x)+sin⁡(x))2sin⁡3(x)−2sin⁡(x)cos⁡(x))sin⁡(x)log⁡(x)cos⁡(x)+3(3log⁡(x)sin⁡(x)−2cos⁡(x)x)(3sin⁡(x)cos⁡(x)−2xlog⁡(x))sin⁡(x)cos⁡(x)+(3log⁡(x)sin⁡(x)−2cos⁡(x)x)(12sin⁡2(x)cos⁡2(x)+3−12sin⁡(x)xlog⁡(x)cos⁡(x)+2x2log⁡(x)+6x2log⁡(x)2)+21(3log⁡(x)sin⁡(x)−2cos⁡(x)x)sin⁡2(x)cos⁡2(x)+(3sin⁡(x)cos⁡(x)−2xlog⁡(x))(−6log⁡(x)2sin⁡2(x)+3log⁡(x)2cos⁡2(x)+12log⁡(x)sin⁡(x)cos⁡(x)x+2log⁡(x)cos⁡2(x)x2−2cos⁡2(x)x2)log⁡(x)cos⁡(x)+9(−6log⁡(x)2sin⁡2(x)+3log⁡(x)2cos⁡2(x)+12log⁡(x)sin⁡(x)cos⁡(x)x+2log⁡(x)cos⁡2(x)x2−2cos⁡2(x)x2)sin⁡(x)log⁡(x)cos⁡2(x)+6log⁡(x)2sin⁡3(x)−21log⁡(x)2sin⁡(x)cos⁡2(x)−36log⁡(x)sin⁡2(x)cos⁡(x)x+18log⁡(x)cos⁡3(x)x−18log⁡(x)sin⁡(x)cos⁡2(x)x2+18sin⁡(x)cos⁡2(x)x2−4log⁡(x)cos⁡3(x)x3+6cos⁡3(x)x3log⁡(x)cos⁡2(x)+9log⁡(x)sin⁡(x)−2(3log⁡(x)sin⁡(x)−2cos⁡(x)x)(3sin⁡(x)cos⁡(x)−2xlog⁡(x))xlog⁡(x)−24(3log⁡(x)sin⁡(x)−2cos⁡(x)x)sin⁡(x)xlog⁡(x)cos⁡(x)−6(−6log⁡(x)2sin⁡2(x)+3log⁡(x)2cos⁡2(x)+12log⁡(x)sin⁡(x)cos⁡(x)x+2log⁡(x)cos⁡2(x)x2−2cos⁡2(x)x2)xlog⁡(x)2cos⁡(x)−6cos⁡(x)x+2(3log⁡(x)sin⁡(x)−2cos⁡(x)x)x2log⁡(x)+10(3log⁡(x)sin⁡(x)−2cos⁡(x)x)x2log⁡(x)2log⁡(x)cos⁡(x)+135sin⁡3(x)−270sin⁡(x)cos⁡2(x))e−15xsin⁡3(x)log⁡(x)2cos⁡3(x)\frac{\left(315 x \sin^{2}{\left(x \right)} \cos{\left(x \right)} - 90 x \cos^{3}{\left(x \right)} - 3375 \left(3 x \cos{\left(x \right)} + \sin{\left(x \right)}\right)^{3} \sin^{6}{\left(x \right)} + 2025 \left(3 x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \left(- x \sin^{2}{\left(x \right)} + 2 x \cos^{2}{\left(x \right)} + 2 \sin{\left(x \right)} \cos{\left(x \right)}\right) \sin^{3}{\left(x \right)} - \frac{45 \left(3 x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \left(\left(3 \log{\left(x \right)} \sin{\left(x \right)} - \frac{2 \cos{\left(x \right)}}{x}\right) \left(\frac{3 \sin{\left(x \right)}}{\cos{\left(x \right)}} - \frac{2}{x \log{\left(x \right)}}\right) + \frac{3 \left(3 \log{\left(x \right)} \sin{\left(x \right)} - \frac{2 \cos{\left(x \right)}}{x}\right) \sin{\left(x \right)}}{\cos{\left(x \right)}} + \frac{- 6 \log{\left(x \right)}^{2} \sin^{2}{\left(x \right)} + 3 \log{\left(x \right)}^{2} \cos^{2}{\left(x \right)} + \frac{12 \log{\left(x \right)} \sin{\left(x \right)} \cos{\left(x \right)}}{x} + \frac{2 \log{\left(x \right)} \cos^{2}{\left(x \right)}}{x^{2}} - \frac{2 \cos^{2}{\left(x \right)}}{x^{2}}}{\log{\left(x \right)} \cos{\left(x \right)}} - \frac{2 \left(3 \log{\left(x \right)} \sin{\left(x \right)} - \frac{2 \cos{\left(x \right)}}{x}\right)}{x \log{\left(x \right)}}\right) \sin^{2}{\left(x \right)}}{\log{\left(x \right)} \cos{\left(x \right)}} + \frac{135 \left(3 \log{\left(x \right)} \sin{\left(x \right)} - \frac{2 \cos{\left(x \right)}}{x}\right) \left(x \sin^{2}{\left(x \right)} - 2 x \cos^{2}{\left(x \right)} + 5 \left(3 x \cos{\left(x \right)} + \sin{\left(x \right)}\right)^{2} \sin^{3}{\left(x \right)} - 2 \sin{\left(x \right)} \cos{\left(x \right)}\right) \sin{\left(x \right)}}{\log{\left(x \right)} \cos{\left(x \right)}} + \frac{\frac{3 \left(3 \log{\left(x \right)} \sin{\left(x \right)} - \frac{2 \cos{\left(x \right)}}{x}\right) \left(\frac{3 \sin{\left(x \right)}}{\cos{\left(x \right)}} - \frac{2}{x \log{\left(x \right)}}\right) \sin{\left(x \right)}}{\cos{\left(x \right)}} + \left(3 \log{\left(x \right)} \sin{\left(x \right)} - \frac{2 \cos{\left(x \right)}}{x}\right) \left(\frac{12 \sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} + 3 - \frac{12 \sin{\left(x \right)}}{x \log{\left(x \right)} \cos{\left(x \right)}} + \frac{2}{x^{2} \log{\left(x \right)}} + \frac{6}{x^{2} \log{\left(x \right)}^{2}}\right) + \frac{21 \left(3 \log{\left(x \right)} \sin{\left(x \right)} - \frac{2 \cos{\left(x \right)}}{x}\right) \sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} + \frac{\left(\frac{3 \sin{\left(x \right)}}{\cos{\left(x \right)}} - \frac{2}{x \log{\left(x \right)}}\right) \left(- 6 \log{\left(x \right)}^{2} \sin^{2}{\left(x \right)} + 3 \log{\left(x \right)}^{2} \cos^{2}{\left(x \right)} + \frac{12 \log{\left(x \right)} \sin{\left(x \right)} \cos{\left(x \right)}}{x} + \frac{2 \log{\left(x \right)} \cos^{2}{\left(x \right)}}{x^{2}} - \frac{2 \cos^{2}{\left(x \right)}}{x^{2}}\right)}{\log{\left(x \right)} \cos{\left(x \right)}} + \frac{9 \left(- 6 \log{\left(x \right)}^{2} \sin^{2}{\left(x \right)} + 3 \log{\left(x \right)}^{2} \cos^{2}{\left(x \right)} + \frac{12 \log{\left(x \right)} \sin{\left(x \right)} \cos{\left(x \right)}}{x} + \frac{2 \log{\left(x \right)} \cos^{2}{\left(x \right)}}{x^{2}} - \frac{2 \cos^{2}{\left(x \right)}}{x^{2}}\right) \sin{\left(x \right)}}{\log{\left(x \right)} \cos^{2}{\left(x \right)}} + \frac{6 \log{\left(x \right)}^{2} \sin^{3}{\left(x \right)} - 21 \log{\left(x \right)}^{2} \sin{\left(x \right)} \cos^{2}{\left(x \right)} - \frac{36 \log{\left(x \right)} \sin^{2}{\left(x \right)} \cos{\left(x \right)}}{x} + \frac{18 \log{\left(x \right)} \cos^{3}{\left(x \right)}}{x} - \frac{18 \log{\left(x \right)} \sin{\left(x \right)} \cos^{2}{\left(x \right)}}{x^{2}} + \frac{18 \sin{\left(x \right)} \cos^{2}{\left(x \right)}}{x^{2}} - \frac{4 \log{\left(x \right)} \cos^{3}{\left(x \right)}}{x^{3}} + \frac{6 \cos^{3}{\left(x \right)}}{x^{3}}}{\log{\left(x \right)} \cos^{2}{\left(x \right)}} + 9 \log{\left(x \right)} \sin{\left(x \right)} - \frac{2 \left(3 \log{\left(x \right)} \sin{\left(x \right)} - \frac{2 \cos{\left(x \right)}}{x}\right) \left(\frac{3 \sin{\left(x \right)}}{\cos{\left(x \right)}} - \frac{2}{x \log{\left(x \right)}}\right)}{x \log{\left(x \right)}} - \frac{24 \left(3 \log{\left(x \right)} \sin{\left(x \right)} - \frac{2 \cos{\left(x \right)}}{x}\right) \sin{\left(x \right)}}{x \log{\left(x \right)} \cos{\left(x \right)}} - \frac{6 \left(- 6 \log{\left(x \right)}^{2} \sin^{2}{\left(x \right)} + 3 \log{\left(x \right)}^{2} \cos^{2}{\left(x \right)} + \frac{12 \log{\left(x \right)} \sin{\left(x \right)} \cos{\left(x \right)}}{x} + \frac{2 \log{\left(x \right)} \cos^{2}{\left(x \right)}}{x^{2}} - \frac{2 \cos^{2}{\left(x \right)}}{x^{2}}\right)}{x \log{\left(x \right)}^{2} \cos{\left(x \right)}} - \frac{6 \cos{\left(x \right)}}{x} + \frac{2 \left(3 \log{\left(x \right)} \sin{\left(x \right)} - \frac{2 \cos{\left(x \right)}}{x}\right)}{x^{2} \log{\left(x \right)}} + \frac{10 \left(3 \log{\left(x \right)} \sin{\left(x \right)} - \frac{2 \cos{\left(x \right)}}{x}\right)}{x^{2} \log{\left(x \right)}^{2}}}{\log{\left(x \right)} \cos{\left(x \right)}} + 135 \sin^{3}{\left(x \right)} - 270 \sin{\left(x \right)} \cos^{2}{\left(x \right)}\right) e^{- 15 x \sin^{3}{\left(x \right)}}}{\log{\left(x \right)}^{2} \cos^{3}{\left(x \right)}}
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Gráfico
Derivada de y=(e^(-15x*sinx^3))/((cos^3)lg*x^2)
    © Sr Examen – Калькулятор