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Derivada de:
Derivada de b
Derivada de (3x+6)^2
Derivada de 2*y-4
Derivada de 1/rootx
Expresiones idénticas
x*sin(x/ tres)*sin(x+ cinco)*cos(x- seis)*sin(x+ siete)*cos(x- ocho)
x multiplicar por seno de (x dividir por 3) multiplicar por seno de (x más 5) multiplicar por coseno de (x menos 6) multiplicar por seno de (x más 7) multiplicar por coseno de (x menos 8)
x multiplicar por seno de (x dividir por tres) multiplicar por seno de (x más cinco) multiplicar por coseno de (x menos seis) multiplicar por seno de (x más siete) multiplicar por coseno de (x menos ocho)
xsin(x/3)sin(x+5)cos(x-6)sin(x+7)cos(x-8)
xsinx/3sinx+5cosx-6sinx+7cosx-8
x*sin(x dividir por 3)*sin(x+5)*cos(x-6)*sin(x+7)*cos(x-8)
Expresiones semejantes
x*sin(x/3)*sin(x+5)*cos(x-6)*sin(x-7)*cos(x-8)
x*sin(x/3)*sin(x-5)*cos(x-6)*sin(x+7)*cos(x-8)
x*sin(x/3)*sin(x+5)*cos(x-6)*sin(x+7)*cos(x+8)
x*sin(x/3)*sin(x+5)*cos(x+6)*sin(x+7)*cos(x-8)

Derivada de la función/ x*sin(x/3)*sin(x+5)*cos(x-6)*sin(x+7)*cos(x-8)

Derivada de xsin(x/3)sin(x+5)cos(x-6)sin(x+7)*cos(x-8)

Solución

Ha introducido [src]

     /x\                                            
x*sin|-|*sin(x + 5)*cos(x - 6)*sin(x + 7)*cos(x - 8)
     \3/

x \sin{\left(\frac{x}{3} \right)} \sin{\left(x + 5 \right)} \cos{\left(x - 6 \right)} \sin{\left(x + 7 \right)} \cos{\left(x - 8 \right)}

((((x*sin(x/3))*sin(x + 5))*cos(x - 6))*sin(x + 7))*cos(x - 8)

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

////     /x\         \                                 \                                            \                                                       \                                                                  
||||x*cos|-|         |                                 |                                            |                                                       |                                                                  
||||     \3/      /x\|                              /x\|                   /x\                      |                                         /x\           |                              /x\                                 
||||-------- + sin|-||*sin(x + 5) + x*cos(x + 5)*sin|-||*cos(x - 6) - x*sin|-|*sin(x - 6)*sin(x + 5)|*sin(x + 7) + x*cos(x - 6)*cos(x + 7)*sin|-|*sin(x + 5)|*cos(x - 8) - x*cos(x - 6)*sin|-|*sin(x - 8)*sin(x + 5)*sin(x + 7)
\\\\   3          \3//                              \3//                   \3/                      /                                         \3/           /                              \3/

- x \sin{\left(\frac{x}{3} \right)} \sin{\left(x - 8 \right)} \sin{\left(x + 5 \right)} \sin{\left(x + 7 \right)} \cos{\left(x - 6 \right)} + \left(x \sin{\left(\frac{x}{3} \right)} \sin{\left(x + 5 \right)} \cos{\left(x - 6 \right)} \cos{\left(x + 7 \right)} + \left(- x \sin{\left(\frac{x}{3} \right)} \sin{\left(x - 6 \right)} \sin{\left(x + 5 \right)} + \left(x \sin{\left(\frac{x}{3} \right)} \cos{\left(x + 5 \right)} + \left(\frac{x \cos{\left(\frac{x}{3} \right)}}{3} + \sin{\left(\frac{x}{3} \right)}\right) \sin{\left(x + 5 \right)}\right) \cos{\left(x - 6 \right)}\right) \sin{\left(x + 7 \right)}\right) \cos{\left(x - 8 \right)}

Simplificar

Segunda derivada [src]

 /////       /x\        /x\\                /     /x\        /x\\                     /x\           \                 //     /x\        /x\\                                /x\\                                  /x\           \                /  //     /x\        /x\\                                /x\\                      /x\                       \                                 /x\                      \                 /  /  //     /x\        /x\\                                /x\\                      /x\                       \                                            /x\           \                                                                     \
 |||||- 6*cos|-| + x*sin|-||*sin(5 + x) - 6*|3*sin|-| + x*cos|-||*cos(5 + x) + 9*x*sin|-|*sin(5 + x)|*cos(-6 + x) + 6*||3*sin|-| + x*cos|-||*sin(5 + x) + 3*x*cos(5 + x)*sin|-||*sin(-6 + x) + 9*x*cos(-6 + x)*sin|-|*sin(5 + x)|*sin(7 + x) + 6*|- ||3*sin|-| + x*cos|-||*sin(5 + x) + 3*x*cos(5 + x)*sin|-||*cos(-6 + x) + 3*x*sin|-|*sin(-6 + x)*sin(5 + x)|*cos(7 + x) + 9*x*cos(-6 + x)*sin|-|*sin(5 + x)*sin(7 + x)|*cos(-8 + x)   2*|- |- ||3*sin|-| + x*cos|-||*sin(5 + x) + 3*x*cos(5 + x)*sin|-||*cos(-6 + x) + 3*x*sin|-|*sin(-6 + x)*sin(5 + x)|*sin(7 + x) + 3*x*cos(-6 + x)*cos(7 + x)*sin|-|*sin(5 + x)|*sin(-8 + x)                                                         |
 |\\\\       \3/        \3//                \     \3/        \3//                     \3/           /                 \\     \3/        \3//                                \3//                                  \3/           /                \  \\     \3/        \3//                                \3//                      \3/                       /                                 \3/                      /                 \  \  \\     \3/        \3//                                \3//                      \3/                       /                                            \3/           /                                            /x\                      |
-|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + x*cos(-8 + x)*cos(-6 + x)*sin|-|*sin(5 + x)*sin(7 + x)|
 \                                                                                                                                                                                                                 9                                                                                                                                                                                                                                                                                                                 3                                                                                                                             \3/                      /

- (x \sin{\left(\frac{x}{3} \right)} \sin{\left(x + 5 \right)} \sin{\left(x + 7 \right)} \cos{\left(x - 8 \right)} \cos{\left(x - 6 \right)} + \frac{2 \left(3 x \sin{\left(\frac{x}{3} \right)} \sin{\left(x + 5 \right)} \cos{\left(x - 6 \right)} \cos{\left(x + 7 \right)} - \left(3 x \sin{\left(\frac{x}{3} \right)} \sin{\left(x - 6 \right)} \sin{\left(x + 5 \right)} - \left(3 x \sin{\left(\frac{x}{3} \right)} \cos{\left(x + 5 \right)} + \left(x \cos{\left(\frac{x}{3} \right)} + 3 \sin{\left(\frac{x}{3} \right)}\right) \sin{\left(x + 5 \right)}\right) \cos{\left(x - 6 \right)}\right) \sin{\left(x + 7 \right)}\right) \sin{\left(x - 8 \right)}}{3} + \frac{\left(9 x \sin{\left(\frac{x}{3} \right)} \sin{\left(x + 5 \right)} \sin{\left(x + 7 \right)} \cos{\left(x - 6 \right)} + 6 \left(3 x \sin{\left(\frac{x}{3} \right)} \sin{\left(x - 6 \right)} \sin{\left(x + 5 \right)} - \left(3 x \sin{\left(\frac{x}{3} \right)} \cos{\left(x + 5 \right)} + \left(x \cos{\left(\frac{x}{3} \right)} + 3 \sin{\left(\frac{x}{3} \right)}\right) \sin{\left(x + 5 \right)}\right) \cos{\left(x - 6 \right)}\right) \cos{\left(x + 7 \right)} + \left(9 x \sin{\left(\frac{x}{3} \right)} \sin{\left(x + 5 \right)} \cos{\left(x - 6 \right)} + 6 \left(3 x \sin{\left(\frac{x}{3} \right)} \cos{\left(x + 5 \right)} + \left(x \cos{\left(\frac{x}{3} \right)} + 3 \sin{\left(\frac{x}{3} \right)}\right) \sin{\left(x + 5 \right)}\right) \sin{\left(x - 6 \right)} + \left(9 x \sin{\left(\frac{x}{3} \right)} \sin{\left(x + 5 \right)} + \left(x \sin{\left(\frac{x}{3} \right)} - 6 \cos{\left(\frac{x}{3} \right)}\right) \sin{\left(x + 5 \right)} - 6 \left(x \cos{\left(\frac{x}{3} \right)} + 3 \sin{\left(\frac{x}{3} \right)}\right) \cos{\left(x + 5 \right)}\right) \cos{\left(x - 6 \right)}\right) \sin{\left(x + 7 \right)}\right) \cos{\left(x - 8 \right)}}{9})

Simplificar

Tercera derivada [src]

                                                                                                                                                                                             /  /  //     /x\        /x\\                /       /x\        /x\\                 /     /x\        /x\\                                 /x\\                  //     /x\        /x\\                                /x\\                 //       /x\        /x\\                /     /x\        /x\\                     /x\           \                       /x\                       \                 /  //     /x\        /x\\                                /x\\                      /x\                       \                ///       /x\        /x\\                /     /x\        /x\\                     /x\           \                 //     /x\        /x\\                                /x\\                                  /x\           \                                             /x\           \               ////       /x\        /x\\                /     /x\        /x\\                     /x\           \                 //     /x\        /x\\                                /x\\                                  /x\           \                /  //     /x\        /x\\                                /x\\                      /x\                       \                                 /x\                      \                                                                     
                                                                                                                                                                                             |- |- ||9*sin|-| + x*cos|-||*sin(5 + x) + 9*|- 6*cos|-| + x*sin|-||*cos(5 + x) + 27*|3*sin|-| + x*cos|-||*sin(5 + x) + 27*x*cos(5 + x)*sin|-||*cos(-6 + x) - 27*||3*sin|-| + x*cos|-||*sin(5 + x) + 3*x*cos(5 + x)*sin|-||*cos(-6 + x) + 9*||- 6*cos|-| + x*sin|-||*sin(5 + x) - 6*|3*sin|-| + x*cos|-||*cos(5 + x) + 9*x*sin|-|*sin(5 + x)|*sin(-6 + x) + 27*x*sin|-|*sin(-6 + x)*sin(5 + x)|*sin(7 + x) - 27*|- ||3*sin|-| + x*cos|-||*sin(5 + x) + 3*x*cos(5 + x)*sin|-||*cos(-6 + x) + 3*x*sin|-|*sin(-6 + x)*sin(5 + x)|*sin(7 + x) + 9*|||- 6*cos|-| + x*sin|-||*sin(5 + x) - 6*|3*sin|-| + x*cos|-||*cos(5 + x) + 9*x*sin|-|*sin(5 + x)|*cos(-6 + x) + 6*||3*sin|-| + x*cos|-||*sin(5 + x) + 3*x*cos(5 + x)*sin|-||*sin(-6 + x) + 9*x*cos(-6 + x)*sin|-|*sin(5 + x)|*cos(7 + x) + 27*x*cos(-6 + x)*cos(7 + x)*sin|-|*sin(5 + x)|*cos(-8 + x)   ||||- 6*cos|-| + x*sin|-||*sin(5 + x) - 6*|3*sin|-| + x*cos|-||*cos(5 + x) + 9*x*sin|-|*sin(5 + x)|*cos(-6 + x) + 6*||3*sin|-| + x*cos|-||*sin(5 + x) + 3*x*cos(5 + x)*sin|-||*sin(-6 + x) + 9*x*cos(-6 + x)*sin|-|*sin(5 + x)|*sin(7 + x) + 6*|- ||3*sin|-| + x*cos|-||*sin(5 + x) + 3*x*cos(5 + x)*sin|-||*cos(-6 + x) + 3*x*sin|-|*sin(-6 + x)*sin(5 + x)|*cos(7 + x) + 9*x*cos(-6 + x)*sin|-|*sin(5 + x)*sin(7 + x)|*sin(-8 + x)                                                         
  /  /  //     /x\        /x\\                                /x\\                      /x\                       \                                            /x\           \               \  \  \\     \3/        \3//                \       \3/        \3//                 \     \3/        \3//                                 \3//                  \\     \3/        \3//                                \3//                 \\       \3/        \3//                \     \3/        \3//                     \3/           /                       \3/                       /                 \  \\     \3/        \3//                                \3//                      \3/                       /                \\\       \3/        \3//                \     \3/        \3//                     \3/           /                 \\     \3/        \3//                                \3//                                  \3/           /                                             \3/           /               \\\\       \3/        \3//                \     \3/        \3//                     \3/           /                 \\     \3/        \3//                                \3//                                  \3/           /                \  \\     \3/        \3//                                \3//                      \3/                       /                                 \3/                      /                                /x\                                  
- |- |- ||3*sin|-| + x*cos|-||*sin(5 + x) + 3*x*cos(5 + x)*sin|-||*cos(-6 + x) + 3*x*sin|-|*sin(-6 + x)*sin(5 + x)|*sin(7 + x) + 3*x*cos(-6 + x)*cos(7 + x)*sin|-|*sin(5 + x)|*cos(-8 + x) - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + x*cos(-6 + x)*sin|-|*sin(-8 + x)*sin(5 + x)*sin(7 + x)
  \  \  \\     \3/        \3//                                \3//                      \3/                       /                                            \3/           /                                                                                                                                                                                                                                                                                                                                                                                                                                        27                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            3                                                                                                                                                                                                                                      \3/

x \sin{\left(\frac{x}{3} \right)} \sin{\left(x - 8 \right)} \sin{\left(x + 5 \right)} \sin{\left(x + 7 \right)} \cos{\left(x - 6 \right)} - \left(3 x \sin{\left(\frac{x}{3} \right)} \sin{\left(x + 5 \right)} \cos{\left(x - 6 \right)} \cos{\left(x + 7 \right)} - \left(3 x \sin{\left(\frac{x}{3} \right)} \sin{\left(x - 6 \right)} \sin{\left(x + 5 \right)} - \left(3 x \sin{\left(\frac{x}{3} \right)} \cos{\left(x + 5 \right)} + \left(x \cos{\left(\frac{x}{3} \right)} + 3 \sin{\left(\frac{x}{3} \right)}\right) \sin{\left(x + 5 \right)}\right) \cos{\left(x - 6 \right)}\right) \sin{\left(x + 7 \right)}\right) \cos{\left(x - 8 \right)} + \frac{\left(9 x \sin{\left(\frac{x}{3} \right)} \sin{\left(x + 5 \right)} \sin{\left(x + 7 \right)} \cos{\left(x - 6 \right)} + 6 \left(3 x \sin{\left(\frac{x}{3} \right)} \sin{\left(x - 6 \right)} \sin{\left(x + 5 \right)} - \left(3 x \sin{\left(\frac{x}{3} \right)} \cos{\left(x + 5 \right)} + \left(x \cos{\left(\frac{x}{3} \right)} + 3 \sin{\left(\frac{x}{3} \right)}\right) \sin{\left(x + 5 \right)}\right) \cos{\left(x - 6 \right)}\right) \cos{\left(x + 7 \right)} + \left(9 x \sin{\left(\frac{x}{3} \right)} \sin{\left(x + 5 \right)} \cos{\left(x - 6 \right)} + 6 \left(3 x \sin{\left(\frac{x}{3} \right)} \cos{\left(x + 5 \right)} + \left(x \cos{\left(\frac{x}{3} \right)} + 3 \sin{\left(\frac{x}{3} \right)}\right) \sin{\left(x + 5 \right)}\right) \sin{\left(x - 6 \right)} + \left(9 x \sin{\left(\frac{x}{3} \right)} \sin{\left(x + 5 \right)} + \left(x \sin{\left(\frac{x}{3} \right)} - 6 \cos{\left(\frac{x}{3} \right)}\right) \sin{\left(x + 5 \right)} - 6 \left(x \cos{\left(\frac{x}{3} \right)} + 3 \sin{\left(\frac{x}{3} \right)}\right) \cos{\left(x + 5 \right)}\right) \cos{\left(x - 6 \right)}\right) \sin{\left(x + 7 \right)}\right) \sin{\left(x - 8 \right)}}{3} - \frac{\left(27 x \sin{\left(\frac{x}{3} \right)} \sin{\left(x + 5 \right)} \cos{\left(x - 6 \right)} \cos{\left(x + 7 \right)} - 27 \left(3 x \sin{\left(\frac{x}{3} \right)} \sin{\left(x - 6 \right)} \sin{\left(x + 5 \right)} - \left(3 x \sin{\left(\frac{x}{3} \right)} \cos{\left(x + 5 \right)} + \left(x \cos{\left(\frac{x}{3} \right)} + 3 \sin{\left(\frac{x}{3} \right)}\right) \sin{\left(x + 5 \right)}\right) \cos{\left(x - 6 \right)}\right) \sin{\left(x + 7 \right)} + 9 \left(9 x \sin{\left(\frac{x}{3} \right)} \sin{\left(x + 5 \right)} \cos{\left(x - 6 \right)} + 6 \left(3 x \sin{\left(\frac{x}{3} \right)} \cos{\left(x + 5 \right)} + \left(x \cos{\left(\frac{x}{3} \right)} + 3 \sin{\left(\frac{x}{3} \right)}\right) \sin{\left(x + 5 \right)}\right) \sin{\left(x - 6 \right)} + \left(9 x \sin{\left(\frac{x}{3} \right)} \sin{\left(x + 5 \right)} + \left(x \sin{\left(\frac{x}{3} \right)} - 6 \cos{\left(\frac{x}{3} \right)}\right) \sin{\left(x + 5 \right)} - 6 \left(x \cos{\left(\frac{x}{3} \right)} + 3 \sin{\left(\frac{x}{3} \right)}\right) \cos{\left(x + 5 \right)}\right) \cos{\left(x - 6 \right)}\right) \cos{\left(x + 7 \right)} - \left(27 x \sin{\left(\frac{x}{3} \right)} \sin{\left(x - 6 \right)} \sin{\left(x + 5 \right)} - 27 \left(3 x \sin{\left(\frac{x}{3} \right)} \cos{\left(x + 5 \right)} + \left(x \cos{\left(\frac{x}{3} \right)} + 3 \sin{\left(\frac{x}{3} \right)}\right) \sin{\left(x + 5 \right)}\right) \cos{\left(x - 6 \right)} + 9 \left(9 x \sin{\left(\frac{x}{3} \right)} \sin{\left(x + 5 \right)} + \left(x \sin{\left(\frac{x}{3} \right)} - 6 \cos{\left(\frac{x}{3} \right)}\right) \sin{\left(x + 5 \right)} - 6 \left(x \cos{\left(\frac{x}{3} \right)} + 3 \sin{\left(\frac{x}{3} \right)}\right) \cos{\left(x + 5 \right)}\right) \sin{\left(x - 6 \right)} - \left(27 x \sin{\left(\frac{x}{3} \right)} \cos{\left(x + 5 \right)} + 9 \left(x \sin{\left(\frac{x}{3} \right)} - 6 \cos{\left(\frac{x}{3} \right)}\right) \cos{\left(x + 5 \right)} + 27 \left(x \cos{\left(\frac{x}{3} \right)} + 3 \sin{\left(\frac{x}{3} \right)}\right) \sin{\left(x + 5 \right)} + \left(x \cos{\left(\frac{x}{3} \right)} + 9 \sin{\left(\frac{x}{3} \right)}\right) \sin{\left(x + 5 \right)}\right) \cos{\left(x - 6 \right)}\right) \sin{\left(x + 7 \right)}\right) \cos{\left(x - 8 \right)}}{27}

Simplificar

Gráfico

Derivada de x*sin(x/3)*sin(x+5)*cos(x-6)*sin(x+7)*cos(x-8)

Otras calculadoras

¿Cómo usar?

Expresiones idénticas

Expresiones semejantes

Derivada de xsin(x/3)sin(x+5)cos(x-6)sin(x+7)*cos(x-8)

Gráfico:

Definida a trozos:

Solución

Otras calculadoras

¿Cómo usar?

Expresiones idénticas

Expresiones semejantes

Derivada de x*sin(x/3)*sin(x+5)*cos(x-6)*sin(x+7)*cos(x-8)

Gráfico:

Definida a trozos:

Solución

Derivada de xsin(x/3)sin(x+5)cos(x-6)sin(x+7)*cos(x-8)