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Derivada de:
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Derivada de i*n*x
Derivada de 3^-x
Derivada de y=6x
Expresiones idénticas
cos(sqrt(cuatro *x/log(x)))
coseno de ( raíz cuadrada de (4 multiplicar por x dividir por logaritmo de (x)))
coseno de ( raíz cuadrada de (cuatro multiplicar por x dividir por logaritmo de (x)))
cos(√(4*x/log(x)))
cos(sqrt(4x/log(x)))
cossqrt4x/logx
cos(sqrt(4*x dividir por log(x)))
Expresiones con funciones
Coseno cos
cos(x+3)
cos(x-2)
cos(√sin(tanπx))
cos√(sin(tan(πx)))
cos(e^(2*x))
Raíz cuadrada sqrt
sqrt(x)+1/x
sqrt(x^4-3*x)
sqrt((x)^2+1)*cos(6*x)
sqrt(x)+1/(sqrt(x))
sqrt(x)/(4+x)
Logaritmo log
log((x+1)/(x-1))
log(tanx)
log(y^2-1)
log(x*sin(x)+cos(x))+sqrt(x*sin(x)+cos(x))^2+1
log(x)/e^x

Derivada de la función/ log(x)/ cos(sqrt(4*x/log(x)))

Derivada de cos(sqrt(4*x/log(x)))

Solución

Ha introducido [src]

   /    ________\
   |   /  4*x   |
cos|  /  ------ |
   \\/   log(x) /

\cos{\left(\sqrt{\frac{4 x}{\log{\left(x \right)}}} \right)}

cos(sqrt((4*x)/log(x)))

Solución detallada

Sustituimos $u = \sqrt{\frac{4 x}{\log{\left(x \right)}}}$ .
La derivada del coseno es igual a menos el seno:

$\frac{d}{d u} \cos{\left(u \right)} = - \sin{\left(u \right)}$
Luego se aplica una cadena de reglas. Multiplicamos por $\frac{d}{d x} \sqrt{\frac{4 x}{\log{\left(x \right)}}}$ :
1. Sustituimos $u = \frac{4 x}{\log{\left(x \right)}}$ .
2. Según el principio, aplicamos: $\sqrt{u}$ tenemos $\frac{1}{2 \sqrt{u}}$
3. Luego se aplica una cadena de reglas. Multiplicamos por $\frac{d}{d x} \frac{4 x}{\log{\left(x \right)}}$ :
  1. Se aplica la regla de la derivada parcial:
    
    $\frac{d}{d x} \frac{f{\left(x \right)}}{g{\left(x \right)}} = \frac{- f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}}{g^{2}{\left(x \right)}}$
    
    $f{\left(x \right)} = 4 x$ y $g{\left(x \right)} = \log{\left(x \right)}$ .
    
    Para calcular $\frac{d}{d x} f{\left(x \right)}$ :
    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: $x$ tenemos $1$
      Entonces, como resultado: $4$
    Para calcular $\frac{d}{d x} g{\left(x \right)}$ :
    1. Derivado $\log{\left(x \right)}$ es $\frac{1}{x}$ .
    Ahora aplicamos la regla de la derivada de una divesión:
    
    $\frac{4 \log{\left(x \right)} - 4}{\log{\left(x \right)}^{2}}$
  Como resultado de la secuencia de reglas:
  
  $\frac{4 \log{\left(x \right)} - 4}{4 \sqrt{\frac{x}{\log{\left(x \right)}}} \log{\left(x \right)}^{2}}$
Como resultado de la secuencia de reglas:

$- \frac{\left(4 \log{\left(x \right)} - 4\right) \sin{\left(\sqrt{\frac{4 x}{\log{\left(x \right)}}} \right)}}{4 \sqrt{\frac{x}{\log{\left(x \right)}}} \log{\left(x \right)}^{2}}$
Simplificamos:

$- \frac{\left(\log{\left(x \right)} - 1\right) \sin{\left(2 \sqrt{\frac{x}{\log{\left(x \right)}}} \right)}}{\sqrt{\frac{x}{\log{\left(x \right)}}} \log{\left(x \right)}^{2}}$

Respuesta:

$- \frac{\left(\log{\left(x \right)} - 1\right) \sin{\left(2 \sqrt{\frac{x}{\log{\left(x \right)}}} \right)}}{\sqrt{\frac{x}{\log{\left(x \right)}}} \log{\left(x \right)}^{2}}$

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

       ________                                /    ________\ 
      /   x     /     2        2   \           |   /  4*x   | 
-2*  /  ------ *|- ------- + ------|*log(x)*sin|  /  ------ | 
   \/   log(x)  |     2      log(x)|           \\/   log(x) / 
                \  log (x)         /                          
--------------------------------------------------------------
                             4*x

- \frac{2 \sqrt{\frac{x}{\log{\left(x \right)}}} \left(\frac{2}{\log{\left(x \right)}} - \frac{2}{\log{\left(x \right)}^{2}}\right) \log{\left(x \right)} \sin{\left(\sqrt{\frac{4 x}{\log{\left(x \right)}}} \right)}}{4 x}

Simplificar

Segunda derivada [src]

              2    /      ________\       ________                 /      ________\       ________             2    /      ________\       ________                 /      ________\       ________                 /      ________\
  /      1   \     |     /   x    |      /   x     /      1   \    |     /   x    |      /   x     /      1   \     |     /   x    |      /   x     /      2   \    |     /   x    |      /   x     /      1   \    |     /   x    |
  |1 - ------| *cos|2*  /  ------ |     /  ------ *|1 - ------|*sin|2*  /  ------ |     /  ------ *|1 - ------| *sin|2*  /  ------ |     /  ------ *|1 - ------|*sin|2*  /  ------ |     /  ------ *|1 - ------|*sin|2*  /  ------ |
  \    log(x)/     \  \/   log(x) /   \/   log(x)  \    log(x)/    \  \/   log(x) /   \/   log(x)  \    log(x)/     \  \/   log(x) /   \/   log(x)  \    log(x)/    \  \/   log(x) /   \/   log(x)  \    log(x)/    \  \/   log(x) /
- --------------------------------- + --------------------------------------------- - ---------------------------------------------- + --------------------------------------------- - ---------------------------------------------
                log(x)                                      x                                              2*x                                            x*log(x)                                        x*log(x)                  
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                 x

\frac{- \frac{\left(1 - \frac{1}{\log{\left(x \right)}}\right)^{2} \cos{\left(2 \sqrt{\frac{x}{\log{\left(x \right)}}} \right)}}{\log{\left(x \right)}} + \frac{\sqrt{\frac{x}{\log{\left(x \right)}}} \left(1 - \frac{2}{\log{\left(x \right)}}\right) \sin{\left(2 \sqrt{\frac{x}{\log{\left(x \right)}}} \right)}}{x \log{\left(x \right)}} - \frac{\sqrt{\frac{x}{\log{\left(x \right)}}} \left(1 - \frac{1}{\log{\left(x \right)}}\right)^{2} \sin{\left(2 \sqrt{\frac{x}{\log{\left(x \right)}}} \right)}}{2 x} + \frac{\sqrt{\frac{x}{\log{\left(x \right)}}} \left(1 - \frac{1}{\log{\left(x \right)}}\right) \sin{\left(2 \sqrt{\frac{x}{\log{\left(x \right)}}} \right)}}{x} - \frac{\sqrt{\frac{x}{\log{\left(x \right)}}} \left(1 - \frac{1}{\log{\left(x \right)}}\right) \sin{\left(2 \sqrt{\frac{x}{\log{\left(x \right)}}} \right)}}{x \log{\left(x \right)}}}{x}

Simplificar

Tercera derivada [src]

                                                                                                                                                                                                                                                                                                                                                                                 ________                  /      ________\                                                                                                                                                                                                                                                                        
                2    /      ________\                 2    /      ________\                 3    /      ________\       ________             3    /      ________\         ________                 /      ________\                                  /      ________\       ________             3    /      ________\         ________             2    /      ________\      /   x     /       6   \    |     /   x    |         ________                 /      ________\         ________                 /      ________\         ________                 /      ________\         ________             2    /      ________\         ________                              /      ________\
    /      1   \     |     /   x    |     /      1   \     |     /   x    |     /      1   \     |     /   x    |      /   x     /      1   \     |     /   x    |        /   x     /      1   \    |     /   x    |     /      1   \ /      2   \    |     /   x    |      /   x     /      1   \     |     /   x    |        /   x     /      1   \     |     /   x    |     /  ------ *|1 - -------|*sin|2*  /  ------ |        /   x     /      2   \    |     /   x    |        /   x     /      2   \    |     /   x    |        /   x     /      1   \    |     /   x    |        /   x     /      1   \     |     /   x    |        /   x     /      1   \ /      2   \    |     /   x    |
  3*|1 - ------| *cos|2*  /  ------ |   3*|1 - ------| *cos|2*  /  ------ |   3*|1 - ------| *cos|2*  /  ------ |     /  ------ *|1 - ------| *sin|2*  /  ------ |   2*  /  ------ *|1 - ------|*sin|2*  /  ------ |   3*|1 - ------|*|1 - ------|*cos|2*  /  ------ |     /  ------ *|1 - ------| *sin|2*  /  ------ |   3*  /  ------ *|1 - ------| *sin|2*  /  ------ |   \/   log(x)  |       2   |    \  \/   log(x) /   2*  /  ------ *|1 - ------|*sin|2*  /  ------ |   2*  /  ------ *|1 - ------|*sin|2*  /  ------ |   3*  /  ------ *|1 - ------|*sin|2*  /  ------ |   3*  /  ------ *|1 - ------| *sin|2*  /  ------ |   3*  /  ------ *|1 - ------|*|1 - ------|*sin|2*  /  ------ |
    \    log(x)/     \  \/   log(x) /     \    log(x)/     \  \/   log(x) /     \    log(x)/     \  \/   log(x) /   \/   log(x)  \    log(x)/     \  \/   log(x) /     \/   log(x)  \    log(x)/    \  \/   log(x) /     \    log(x)/ \    log(x)/    \  \/   log(x) /   \/   log(x)  \    log(x)/     \  \/   log(x) /     \/   log(x)  \    log(x)/     \  \/   log(x) /                \    log (x)/                         \/   log(x)  \    log(x)/    \  \/   log(x) /     \/   log(x)  \    log(x)/    \  \/   log(x) /     \/   log(x)  \    log(x)/    \  \/   log(x) /     \/   log(x)  \    log(x)/     \  \/   log(x) /     \/   log(x)  \    log(x)/ \    log(x)/    \  \/   log(x) /
- ----------------------------------- + ----------------------------------- - ----------------------------------- + ---------------------------------------------- - ----------------------------------------------- + ----------------------------------------------- - ---------------------------------------------- + ------------------------------------------------ - ---------------------------------------------- - ----------------------------------------------- + ----------------------------------------------- + ----------------------------------------------- - ------------------------------------------------ + ------------------------------------------------------------
                   2                                   log(x)                               2*log(x)                                    log(x)                                              x                                                 2                                               4*x                                               2*x                                             x*log(x)                                          x*log(x)                                              2                                             x*log(x)                                         2*x*log(x)                                               2*x*log(x)                         
                log (x)                                                                                                                                                                                                                    log (x)                                                                                                                                                                                                                                                 x*log (x)                                                                                                                                                                                       
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                                                                                                                                                                                                                  2                                                                                                                                                                                                                                                                                                                                                
                                                                                                                                                                                                                                                                                                                                                 x

\frac{\frac{\sqrt{\frac{x}{\log{\left(x \right)}}} \left(1 - \frac{1}{\log{\left(x \right)}}\right)^{3} \sin{\left(2 \sqrt{\frac{x}{\log{\left(x \right)}}} \right)}}{\log{\left(x \right)}} + \frac{3 \left(1 - \frac{2}{\log{\left(x \right)}}\right) \left(1 - \frac{1}{\log{\left(x \right)}}\right) \cos{\left(2 \sqrt{\frac{x}{\log{\left(x \right)}}} \right)}}{\log{\left(x \right)}^{2}} - \frac{3 \left(1 - \frac{1}{\log{\left(x \right)}}\right)^{3} \cos{\left(2 \sqrt{\frac{x}{\log{\left(x \right)}}} \right)}}{2 \log{\left(x \right)}} + \frac{3 \left(1 - \frac{1}{\log{\left(x \right)}}\right)^{2} \cos{\left(2 \sqrt{\frac{x}{\log{\left(x \right)}}} \right)}}{\log{\left(x \right)}} - \frac{3 \left(1 - \frac{1}{\log{\left(x \right)}}\right)^{2} \cos{\left(2 \sqrt{\frac{x}{\log{\left(x \right)}}} \right)}}{\log{\left(x \right)}^{2}} - \frac{\sqrt{\frac{x}{\log{\left(x \right)}}} \left(1 - \frac{6}{\log{\left(x \right)}^{2}}\right) \sin{\left(2 \sqrt{\frac{x}{\log{\left(x \right)}}} \right)}}{x \log{\left(x \right)}} + \frac{3 \sqrt{\frac{x}{\log{\left(x \right)}}} \left(1 - \frac{2}{\log{\left(x \right)}}\right) \left(1 - \frac{1}{\log{\left(x \right)}}\right) \sin{\left(2 \sqrt{\frac{x}{\log{\left(x \right)}}} \right)}}{2 x \log{\left(x \right)}} - \frac{2 \sqrt{\frac{x}{\log{\left(x \right)}}} \left(1 - \frac{2}{\log{\left(x \right)}}\right) \sin{\left(2 \sqrt{\frac{x}{\log{\left(x \right)}}} \right)}}{x \log{\left(x \right)}} + \frac{2 \sqrt{\frac{x}{\log{\left(x \right)}}} \left(1 - \frac{2}{\log{\left(x \right)}}\right) \sin{\left(2 \sqrt{\frac{x}{\log{\left(x \right)}}} \right)}}{x \log{\left(x \right)}^{2}} - \frac{\sqrt{\frac{x}{\log{\left(x \right)}}} \left(1 - \frac{1}{\log{\left(x \right)}}\right)^{3} \sin{\left(2 \sqrt{\frac{x}{\log{\left(x \right)}}} \right)}}{4 x} + \frac{3 \sqrt{\frac{x}{\log{\left(x \right)}}} \left(1 - \frac{1}{\log{\left(x \right)}}\right)^{2} \sin{\left(2 \sqrt{\frac{x}{\log{\left(x \right)}}} \right)}}{2 x} - \frac{3 \sqrt{\frac{x}{\log{\left(x \right)}}} \left(1 - \frac{1}{\log{\left(x \right)}}\right)^{2} \sin{\left(2 \sqrt{\frac{x}{\log{\left(x \right)}}} \right)}}{2 x \log{\left(x \right)}} - \frac{2 \sqrt{\frac{x}{\log{\left(x \right)}}} \left(1 - \frac{1}{\log{\left(x \right)}}\right) \sin{\left(2 \sqrt{\frac{x}{\log{\left(x \right)}}} \right)}}{x} + \frac{3 \sqrt{\frac{x}{\log{\left(x \right)}}} \left(1 - \frac{1}{\log{\left(x \right)}}\right) \sin{\left(2 \sqrt{\frac{x}{\log{\left(x \right)}}} \right)}}{x \log{\left(x \right)}}}{x^{2}}

Simplificar

Gráfico

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Expresiones idénticas

Expresiones con funciones

Derivada de cos(sqrt(4*x/log(x)))

Gráfico:

Definida a trozos:

Solución