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Expresiones idénticas
xlog2(sin((3x+ cuatro)/(x+ uno)))*exp(-x)
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xlog2(sin((3x+4)/(x+1)))exp(-x)
xlog2sin3x+4/x+1exp-x
xlog2(sin((3x+4) dividir por (x+1)))*exp(-x)
Expresiones semejantes
xlog2(sin((3x+4)/(x+1)))*exp(x)
xlog2(sin((3x-4)/(x+1)))*exp(-x)
xlog2(sin((3x+4)/(x-1)))*exp(-x)
Expresiones con funciones
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Exponente exp
exp(8*x)
exp(3*x)
exp(y)

Derivada de la función/ xlog2(sin((3x+4)/(x+1)))*exp(-x)

Derivada de xlog2(sin((3x+4)/(x+1)))*exp(-x)

Solución

Ha introducido [src]

     /   /3*x + 4\\    
  log|sin|-------||    
     \   \ x + 1 //  -x
x*-----------------*e  
        log(2)

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

(x*(log(sin((3*x + 4)/(x + 1)))/log(2)))*exp(-x)

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

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

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

Simplificar

Segunda derivada [src]

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

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

Simplificar

Tercera derivada [src]

/                                                          /                                       /                                                2                              2                                             \                                \                                                                                                                                       \    
|                                                          |                                       |                       /4 + 3*x\   /    4 + 3*x\     3/4 + 3*x\   /    4 + 3*x\     /4 + 3*x\        2/4 + 3*x\ /    4 + 3*x\|                                |                   /                     /                   /4 + 3*x\      2/4 + 3*x\ /    4 + 3*x\\\                                 |    
|                                                          |                                       |                  3*cos|-------|   |3 - -------| *cos |-------|   |3 - -------| *cos|-------|   3*cos |-------|*|3 - -------||                                |                   |                     |              2*cos|-------|   cos |-------|*|3 - -------|||                                 |    
|                                                          |                                       |    3*(4 + 3*x)        \ 1 + x /   \     1 + x /      \ 1 + x /   \     1 + x /     \ 1 + x /         \ 1 + x / \     1 + x /|                                |                   |                     |    4 + 3*x        \ 1 + x /       \ 1 + x / \     1 + x /||                                 |    
|                                                          |                                   2*x*|9 - ----------- + -------------- + ---------------------------- + --------------------------- + -----------------------------|                                |                   |                   x*|3 - ------- + -------------- + ---------------------------||                                 |    
|                                                          |                       /4 + 3*x\       |       1 + x          /4 + 3*x\              3/4 + 3*x\                      /4 + 3*x\                     2/4 + 3*x\        |        2/4 + 3*x\ /    4 + 3*x\|                   |       /4 + 3*x\     |     1 + x        /4 + 3*x\              2/4 + 3*x\       ||                                 |    
|                                                          |                  6*cos|-------|       |                   sin|-------|           sin |-------|                   sin|-------|                  sin |-------|        |   3*cos |-------|*|3 - -------||                   |  2*cos|-------|     |               sin|-------|           sin |-------|       ||                                 |    
|                                            /    4 + 3*x\ |    3*(4 + 3*x)        \ 1 + x /       \                      \ 1 + x /               \ 1 + x /                      \ 1 + x /                      \ 1 + x /        /         \ 1 + x / \     1 + x /|     /    4 + 3*x\ |       \ 1 + x /     \                  \ 1 + x /               \ 1 + x /       /|                                 |    
|                                            |3 - -------|*|9 - ----------- + -------------- - ----------------------------------------------------------------------------------------------------------------------------------- + -----------------------------|   3*|3 - -------|*|- -------------- + --------------------------------------------------------------|                                 |    
|                                            \     1 + x / |       1 + x          /4 + 3*x\                                                                   1 + x                                                                             2/4 + 3*x\        |     \     1 + x / |      /4 + 3*x\                                1 + x                             |       /    4 + 3*x\    /4 + 3*x\|    
|                                                          |                   sin|-------|                                                                                                                                                  sin |-------|        |                   |   sin|-------|                                                                  |   3*x*|3 - -------|*cos|-------||    
|     /   /4 + 3*x\\        /   /4 + 3*x\\                 \                      \ 1 + x /                                                                                                                                                      \ 1 + x /        /                   \      \ 1 + x /                                                                  /       \     1 + x /    \ 1 + x /|  -x
|3*log|sin|-------|| - x*log|sin|-------|| - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------- + ------------------------------|*e  
|     \   \ 1 + x //        \   \ 1 + x //                                                                                                                 2                                                                                                                                                         1 + x                                                                  /4 + 3*x\     |    
|                                                                                                                                                   (1 + x)                                                                                                                                                                                                                      (1 + x)*sin|-------|     |    
\                                                                                                                                                                                                                                                                                                                                                                                           \ 1 + x /     /    
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                                                                     log(2)

\frac{\left(\frac{3 x \left(3 - \frac{3 x + 4}{x + 1}\right) \cos{\left(\frac{3 x + 4}{x + 1} \right)}}{\left(x + 1\right) \sin{\left(\frac{3 x + 4}{x + 1} \right)}} - x \log{\left(\sin{\left(\frac{3 x + 4}{x + 1} \right)} \right)} + \frac{3 \left(3 - \frac{3 x + 4}{x + 1}\right) \left(\frac{x \left(\frac{\left(3 - \frac{3 x + 4}{x + 1}\right) \cos^{2}{\left(\frac{3 x + 4}{x + 1} \right)}}{\sin^{2}{\left(\frac{3 x + 4}{x + 1} \right)}} + 3 + \frac{2 \cos{\left(\frac{3 x + 4}{x + 1} \right)}}{\sin{\left(\frac{3 x + 4}{x + 1} \right)}} - \frac{3 x + 4}{x + 1}\right)}{x + 1} - \frac{2 \cos{\left(\frac{3 x + 4}{x + 1} \right)}}{\sin{\left(\frac{3 x + 4}{x + 1} \right)}}\right)}{x + 1} - \frac{\left(3 - \frac{3 x + 4}{x + 1}\right) \left(- \frac{2 x \left(\frac{\left(3 - \frac{3 x + 4}{x + 1}\right)^{2} \cos{\left(\frac{3 x + 4}{x + 1} \right)}}{\sin{\left(\frac{3 x + 4}{x + 1} \right)}} + \frac{\left(3 - \frac{3 x + 4}{x + 1}\right)^{2} \cos^{3}{\left(\frac{3 x + 4}{x + 1} \right)}}{\sin^{3}{\left(\frac{3 x + 4}{x + 1} \right)}} + \frac{3 \left(3 - \frac{3 x + 4}{x + 1}\right) \cos^{2}{\left(\frac{3 x + 4}{x + 1} \right)}}{\sin^{2}{\left(\frac{3 x + 4}{x + 1} \right)}} + 9 + \frac{3 \cos{\left(\frac{3 x + 4}{x + 1} \right)}}{\sin{\left(\frac{3 x + 4}{x + 1} \right)}} - \frac{3 \left(3 x + 4\right)}{x + 1}\right)}{x + 1} + \frac{3 \left(3 - \frac{3 x + 4}{x + 1}\right) \cos^{2}{\left(\frac{3 x + 4}{x + 1} \right)}}{\sin^{2}{\left(\frac{3 x + 4}{x + 1} \right)}} + 9 + \frac{6 \cos{\left(\frac{3 x + 4}{x + 1} \right)}}{\sin{\left(\frac{3 x + 4}{x + 1} \right)}} - \frac{3 \left(3 x + 4\right)}{x + 1}\right)}{\left(x + 1\right)^{2}} + 3 \log{\left(\sin{\left(\frac{3 x + 4}{x + 1} \right)} \right)}\right) e^{- x}}{\log{\left(2 \right)}}

Simplificar

Gráfico

Derivada de xlog2(sin((3x+4)/(x+1)))*exp(-x)

Otras calculadoras

¿Cómo usar?

Expresiones idénticas

Expresiones semejantes

Expresiones con funciones

Derivada de xlog2(sin((3x+4)/(x+1)))*exp(-x)

Gráfico:

Definida a trozos:

Solución