Sr Examen

Otras calculadoras

x*sin(x)*tg(1/x)*cos(x)/ctg(x)

  • ¿Cómo usar?

  • Derivada de:
  • Derivada de 7^(3*x-1) Derivada de 7^(3*x-1)
  • Derivada de b Derivada de b
  • 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

  • x*sin(x)*tg(uno /x)*cos(x)/ctg(x)
  • x multiplicar por seno de (x) multiplicar por tg(1 dividir por x) multiplicar por coseno de (x) dividir por ctg(x)
  • x multiplicar por seno de (x) multiplicar por tg(uno dividir por x) multiplicar por coseno de (x) dividir por ctg(x)
  • xsin(x)tg(1/x)cos(x)/ctg(x)
  • xsinxtg1/xcosx/ctgx
  • x*sin(x)*tg(1 dividir por x)*cos(x) dividir por ctg(x)

  • Expresiones semejantes

  • x*sinx*tg(1/x)*cosx/ctg(x)
Derivada de la función/ x*sin(x)*tg(1/x)*cos(x)/ctg(x)

Derivada de x*sin(x)*tg(1/x)*cos(x)/ctg(x)

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
            /1\       
x*sin(x)*tan|-|*cos(x)
            \x/       
----------------------
        cot(x)
xsin⁡(x)tan⁡(1x)cos⁡(x)cot⁡(x)\frac{x \sin{\left(x \right)} \tan{\left(\frac{1}{x} \right)} \cos{\left(x \right)}}{\cot{\left(x \right)}} 
(((x*sin(x))*tan(1/x))*cos(x))/cot(x)
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)=xsin⁡(x)cos⁡(x)tan⁡(1x)f{\left(x \right)} = x \sin{\left(x \right)} \cos{\left(x \right)} \tan{\left(\frac{1}{x} \right)} y g(x)=cot⁡(x)g{\left(x \right)} = \cot{\left(x \right)}.

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

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

      ddxf0⁡(x)f1⁡(x)f2⁡(x)f3⁡(x)=f0⁡(x)f1⁡(x)f2⁡(x)ddxf3⁡(x)+f0⁡(x)f1⁡(x)f3⁡(x)ddxf2⁡(x)+f0⁡(x)f2⁡(x)f3⁡(x)ddxf1⁡(x)+f1⁡(x)f2⁡(x)f3⁡(x)ddxf0⁡(x)\frac{d}{d x} \operatorname{f_{0}}{\left(x \right)} \operatorname{f_{1}}{\left(x \right)} \operatorname{f_{2}}{\left(x \right)} \operatorname{f_{3}}{\left(x \right)} = \operatorname{f_{0}}{\left(x \right)} \operatorname{f_{1}}{\left(x \right)} \operatorname{f_{2}}{\left(x \right)} \frac{d}{d x} \operatorname{f_{3}}{\left(x \right)} + \operatorname{f_{0}}{\left(x \right)} \operatorname{f_{1}}{\left(x \right)} \operatorname{f_{3}}{\left(x \right)} \frac{d}{d x} \operatorname{f_{2}}{\left(x \right)} + \operatorname{f_{0}}{\left(x \right)} \operatorname{f_{2}}{\left(x \right)} \operatorname{f_{3}}{\left(x \right)} \frac{d}{d x} \operatorname{f_{1}}{\left(x \right)} + \operatorname{f_{1}}{\left(x \right)} \operatorname{f_{2}}{\left(x \right)} \operatorname{f_{3}}{\left(x \right)} \frac{d}{d x} \operatorname{f_{0}}{\left(x \right)}

      f0⁡(x)=x\operatorname{f_{0}}{\left(x \right)} = x; calculamos ddxf0⁡(x)\frac{d}{d x} \operatorname{f_{0}}{\left(x \right)}:

      1. Según el principio, aplicamos: xx tenemos 11

      f1⁡(x)=cos⁡(x)\operatorname{f_{1}}{\left(x \right)} = \cos{\left(x \right)}; calculamos ddxf1⁡(x)\frac{d}{d x} \operatorname{f_{1}}{\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)}

      f2⁡(x)=sin⁡(x)\operatorname{f_{2}}{\left(x \right)} = \sin{\left(x \right)}; calculamos ddxf2⁡(x)\frac{d}{d x} \operatorname{f_{2}}{\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)}

      f3⁡(x)=tan⁡(1x)\operatorname{f_{3}}{\left(x \right)} = \tan{\left(\frac{1}{x} \right)}; calculamos ddxf3⁡(x)\frac{d}{d x} \operatorname{f_{3}}{\left(x \right)}:

      1. Reescribimos las funciones para diferenciar:

        tan⁡(1x)=sin⁡(1x)cos⁡(1x)\tan{\left(\frac{1}{x} \right)} = \frac{\sin{\left(\frac{1}{x} \right)}}{\cos{\left(\frac{1}{x} \right)}}

      2. 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)=sin⁡(1x)f{\left(x \right)} = \sin{\left(\frac{1}{x} \right)} y g(x)=cos⁡(1x)g{\left(x \right)} = \cos{\left(\frac{1}{x} \right)}.

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

        1. Sustituimos u=1xu = \frac{1}{x}.

        2. La derivada del seno es igual al coseno:

          ddusin⁡(u)=cos⁡(u)\frac{d}{d u} \sin{\left(u \right)} = \cos{\left(u \right)}

        3. Luego se aplica una cadena de reglas. Multiplicamos por ddx1x\frac{d}{d x} \frac{1}{x}:

          1. Según el principio, aplicamos: 1x\frac{1}{x} tenemos −1x2- \frac{1}{x^{2}}

          Como resultado de la secuencia de reglas:

          −cos⁡(1x)x2- \frac{\cos{\left(\frac{1}{x} \right)}}{x^{2}}

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

        1. Sustituimos u=1xu = \frac{1}{x}.

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

          dducos⁡(u)=−sin⁡(u)\frac{d}{d u} \cos{\left(u \right)} = - \sin{\left(u \right)}

        3. Luego se aplica una cadena de reglas. Multiplicamos por ddx1x\frac{d}{d x} \frac{1}{x}:

          1. Según el principio, aplicamos: 1x\frac{1}{x} tenemos −1x2- \frac{1}{x^{2}}

          Como resultado de la secuencia de reglas:

          sin⁡(1x)x2\frac{\sin{\left(\frac{1}{x} \right)}}{x^{2}}

        Ahora aplicamos la regla de la derivada de una divesión:

        −sin⁡2(1x)x2−cos⁡2(1x)x2cos⁡2(1x)\frac{- \frac{\sin^{2}{\left(\frac{1}{x} \right)}}{x^{2}} - \frac{\cos^{2}{\left(\frac{1}{x} \right)}}{x^{2}}}{\cos^{2}{\left(\frac{1}{x} \right)}}

      Como resultado de: x(−sin⁡2(1x)x2−cos⁡2(1x)x2)sin⁡(x)cos⁡(x)cos⁡2(1x)−xsin⁡2(x)tan⁡(1x)+xcos⁡2(x)tan⁡(1x)+sin⁡(x)cos⁡(x)tan⁡(1x)\frac{x \left(- \frac{\sin^{2}{\left(\frac{1}{x} \right)}}{x^{2}} - \frac{\cos^{2}{\left(\frac{1}{x} \right)}}{x^{2}}\right) \sin{\left(x \right)} \cos{\left(x \right)}}{\cos^{2}{\left(\frac{1}{x} \right)}} - x \sin^{2}{\left(x \right)} \tan{\left(\frac{1}{x} \right)} + x \cos^{2}{\left(x \right)} \tan{\left(\frac{1}{x} \right)} + \sin{\left(x \right)} \cos{\left(x \right)} \tan{\left(\frac{1}{x} \right)}

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

    1. Hay varias formas de calcular esta derivada.

      Method #1

      1. Reescribimos las funciones para diferenciar:

        cot⁡(x)=1tan⁡(x)\cot{\left(x \right)} = \frac{1}{\tan{\left(x \right)}}

      2. Sustituimos u=tan⁡(x)u = \tan{\left(x \right)}.

      3. Según el principio, aplicamos: 1u\frac{1}{u} tenemos −1u2- \frac{1}{u^{2}}

      4. Luego se aplica una cadena de reglas. Multiplicamos por ddxtan⁡(x)\frac{d}{d x} \tan{\left(x \right)}:

        1. ddxtan⁡(x)=1cos⁡2(x)\frac{d}{d x} \tan{\left(x \right)} = \frac{1}{\cos^{2}{\left(x \right)}}

        Como resultado de la secuencia de reglas:

        −sin⁡2(x)+cos⁡2(x)cos⁡2(x)tan⁡2(x)- \frac{\sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)} \tan^{2}{\left(x \right)}}

      Method #2

      1. Reescribimos las funciones para diferenciar:

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

      2. 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)=cos⁡(x)f{\left(x \right)} = \cos{\left(x \right)} y g(x)=sin⁡(x)g{\left(x \right)} = \sin{\left(x \right)}.

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

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

        Ahora aplicamos la regla de la derivada de una divesión:

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

    Ahora aplicamos la regla de la derivada de una divesión:

    x(sin⁡2(x)+cos⁡2(x))sin⁡(x)tan⁡(1x)cos⁡(x)tan⁡2(x)+(x(−sin⁡2(1x)x2−cos⁡2(1x)x2)sin⁡(x)cos⁡(x)cos⁡2(1x)−xsin⁡2(x)tan⁡(1x)+xcos⁡2(x)tan⁡(1x)+sin⁡(x)cos⁡(x)tan⁡(1x))cot⁡(x)cot⁡2(x)\frac{\frac{x \left(\sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)}\right) \sin{\left(x \right)} \tan{\left(\frac{1}{x} \right)}}{\cos{\left(x \right)} \tan^{2}{\left(x \right)}} + \left(\frac{x \left(- \frac{\sin^{2}{\left(\frac{1}{x} \right)}}{x^{2}} - \frac{\cos^{2}{\left(\frac{1}{x} \right)}}{x^{2}}\right) \sin{\left(x \right)} \cos{\left(x \right)}}{\cos^{2}{\left(\frac{1}{x} \right)}} - x \sin^{2}{\left(x \right)} \tan{\left(\frac{1}{x} \right)} + x \cos^{2}{\left(x \right)} \tan{\left(\frac{1}{x} \right)} + \sin{\left(x \right)} \cos{\left(x \right)} \tan{\left(\frac{1}{x} \right)}\right) \cot{\left(x \right)}}{\cot^{2}{\left(x \right)}}

  2. Simplificamos:

    −2xsin⁡3(x)tan⁡(1x)cos⁡(x)+2xtan⁡(1x)tan⁡(x)+sin⁡2(x)tan⁡(1x)−sin⁡2(x)xcos⁡2(1x)- \frac{2 x \sin^{3}{\left(x \right)} \tan{\left(\frac{1}{x} \right)}}{\cos{\left(x \right)}} + 2 x \tan{\left(\frac{1}{x} \right)} \tan{\left(x \right)} + \sin^{2}{\left(x \right)} \tan{\left(\frac{1}{x} \right)} - \frac{\sin^{2}{\left(x \right)}}{x \cos^{2}{\left(\frac{1}{x} \right)}}

Respuesta:

−2xsin⁡3(x)tan⁡(1x)cos⁡(x)+2xtan⁡(1x)tan⁡(x)+sin⁡2(x)tan⁡(1x)−sin⁡2(x)xcos⁡2(1x)- \frac{2 x \sin^{3}{\left(x \right)} \tan{\left(\frac{1}{x} \right)}}{\cos{\left(x \right)}} + 2 x \tan{\left(\frac{1}{x} \right)} \tan{\left(x \right)} + \sin^{2}{\left(x \right)} \tan{\left(\frac{1}{x} \right)} - \frac{\sin^{2}{\left(x \right)}}{x \cos^{2}{\left(\frac{1}{x} \right)}}

Gráfica
02468-8-6-4-2-1010-5050
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
/                             /       2/1\\       \                                                                 
|                             |1 + tan |-||*sin(x)|                                                                 
|                       /1\   \        \x//       |               2       /1\     /       2   \                  /1\
|(x*cos(x) + sin(x))*tan|-| - --------------------|*cos(x) - x*sin (x)*tan|-|   x*\1 + cot (x)/*cos(x)*sin(x)*tan|-|
\                       \x/            x          /                       \x/                                    \x/
----------------------------------------------------------------------------- + ------------------------------------
                                    cot(x)                                                       2                  
                                                                                              cot (x)
x(cot⁡2(x)+1)sin⁡(x)cos⁡(x)tan⁡(1x)cot⁡2(x)+−xsin⁡2(x)tan⁡(1x)+((xcos⁡(x)+sin⁡(x))tan⁡(1x)−(tan⁡2(1x)+1)sin⁡(x)x)cos⁡(x)cot⁡(x)\frac{x \left(\cot^{2}{\left(x \right)} + 1\right) \sin{\left(x \right)} \cos{\left(x \right)} \tan{\left(\frac{1}{x} \right)}}{\cot^{2}{\left(x \right)}} + \frac{- x \sin^{2}{\left(x \right)} \tan{\left(\frac{1}{x} \right)} + \left(\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \tan{\left(\frac{1}{x} \right)} - \frac{\left(\tan^{2}{\left(\frac{1}{x} \right)} + 1\right) \sin{\left(x \right)}}{x}\right) \cos{\left(x \right)}}{\cot{\left(x \right)}}
Simplificar
Segunda derivada [src] 
  /                                                                                      /       /1\\       \                                                                                         /  /                             /       2/1\\       \                          \                                                                                     
  |                                                                                      |    tan|-||       |                                                                                         |  |                             |1 + tan |-||*sin(x)|                          |                                                                                     
  |                                  /       2/1\\                         /       2/1\\ |       \x/|       |            /                             /       2/1\\       \            /       2   \ |  |                       /1\   \        \x//       |               2       /1\|                                                                                     
  |                                2*|1 + tan |-||*(x*cos(x) + sin(x))   2*|1 + tan |-||*|1 + ------|*sin(x)|            |                             |1 + tan |-||*sin(x)|          2*\1 + cot (x)/*|- |(x*cos(x) + sin(x))*tan|-| - --------------------|*cos(x) + x*sin (x)*tan|-||                                              /            2   \                     
  |                          /1\     \        \x//                         \        \x// \      x   /       |            |                       /1\   \        \x//       |                          \  \                       \x/            x          /                       \x//                      /1\       /       2   \ |     1 + cot (x)|                  /1\
- |(-2*cos(x) + x*sin(x))*tan|-| + ----------------------------------- - -----------------------------------|*cos(x) - 2*|(x*cos(x) + sin(x))*tan|-| - --------------------|*sin(x) - ------------------------------------------------------------------------------------------------- - x*cos(x)*sin(x)*tan|-| + 2*x*\1 + cot (x)/*|-1 + -----------|*cos(x)*sin(x)*tan|-|
  |                          \x/                     2                                     2                |            \                       \x/            x          /                                                        cot(x)                                                                   \x/                     |          2     |                  \x/
  \                                                 x                                     x                 /                                                                                                                                                                                                                        \       cot (x)  /                     
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                                                   cot(x)
2x(cot⁡2(x)+1cot⁡2(x)−1)(cot⁡2(x)+1)sin⁡(x)cos⁡(x)tan⁡(1x)−xsin⁡(x)cos⁡(x)tan⁡(1x)−2((xcos⁡(x)+sin⁡(x))tan⁡(1x)−(tan⁡2(1x)+1)sin⁡(x)x)sin⁡(x)−2(xsin⁡2(x)tan⁡(1x)−((xcos⁡(x)+sin⁡(x))tan⁡(1x)−(tan⁡2(1x)+1)sin⁡(x)x)cos⁡(x))(cot⁡2(x)+1)cot⁡(x)−((xsin⁡(x)−2cos⁡(x))tan⁡(1x)−2(1+tan⁡(1x)x)(tan⁡2(1x)+1)sin⁡(x)x2+2(xcos⁡(x)+sin⁡(x))(tan⁡2(1x)+1)x2)cos⁡(x)cot⁡(x)\frac{2 x \left(\frac{\cot^{2}{\left(x \right)} + 1}{\cot^{2}{\left(x \right)}} - 1\right) \left(\cot^{2}{\left(x \right)} + 1\right) \sin{\left(x \right)} \cos{\left(x \right)} \tan{\left(\frac{1}{x} \right)} - x \sin{\left(x \right)} \cos{\left(x \right)} \tan{\left(\frac{1}{x} \right)} - 2 \left(\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \tan{\left(\frac{1}{x} \right)} - \frac{\left(\tan^{2}{\left(\frac{1}{x} \right)} + 1\right) \sin{\left(x \right)}}{x}\right) \sin{\left(x \right)} - \frac{2 \left(x \sin^{2}{\left(x \right)} \tan{\left(\frac{1}{x} \right)} - \left(\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \tan{\left(\frac{1}{x} \right)} - \frac{\left(\tan^{2}{\left(\frac{1}{x} \right)} + 1\right) \sin{\left(x \right)}}{x}\right) \cos{\left(x \right)}\right) \left(\cot^{2}{\left(x \right)} + 1\right)}{\cot{\left(x \right)}} - \left(\left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \tan{\left(\frac{1}{x} \right)} - \frac{2 \left(1 + \frac{\tan{\left(\frac{1}{x} \right)}}{x}\right) \left(\tan^{2}{\left(\frac{1}{x} \right)} + 1\right) \sin{\left(x \right)}}{x^{2}} + \frac{2 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \left(\tan^{2}{\left(\frac{1}{x} \right)} + 1\right)}{x^{2}}\right) \cos{\left(x \right)}}{\cot{\left(x \right)}}
Simplificar
Tercera derivada [src] 
  /                                                                                                                                           /           2/1\        2/1\        /1\\       \                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       
  |                                                                                        /       /1\\                                       |    1 + tan |-|   2*tan |-|   6*tan|-||       |                                                                           /                                                                                      /       /1\\       \                                             //                                                                                      /       /1\\       \                                                                                               \                                                                                                                                                                                                        
  |                                                                                        |    tan|-||                         /       2/1\\ |            \x/         \x/        \x/|       |                                                                           |                                                                                      |    tan|-||       |                                             ||                                                                                      |    tan|-||       |                                                                                               |                                                                                                                                                                                                        
  |                                 /       2/1\\                            /       2/1\\ |       \x/|                       2*|1 + tan |-||*|3 + ----------- + --------- + --------|*sin(x)|            /                             /       2/1\\       \            |                                  /       2/1\\                         /       2/1\\ |       \x/|       |                                             ||                                  /       2/1\\                         /       2/1\\ |       \x/|       |            /                             /       2/1\\       \                                |                                      /  /                             /       2/1\\       \                          \                                                                                 
  |                               3*|1 + tan |-||*(-2*cos(x) + x*sin(x))   6*|1 + tan |-||*|1 + ------|*(x*cos(x) + sin(x))     \        \x// |          2            2         x    |       |            |                             |1 + tan |-||*sin(x)|            |                                2*|1 + tan |-||*(x*cos(x) + sin(x))   2*|1 + tan |-||*|1 + ------|*sin(x)|                                             ||                                2*|1 + tan |-||*(x*cos(x) + sin(x))   2*|1 + tan |-||*|1 + ------|*sin(x)|            |                             |1 + tan |-||*sin(x)|                                |                   /            2   \ |  |                             |1 + tan |-||*sin(x)|                          |                                                                                 
  |                         /1\     \        \x//                            \        \x// \      x   /                                       \         x            x               /       |            |                       /1\   \        \x//       |            |                          /1\     \        \x//                         \        \x// \      x   /       |               2       /1\     /       2   \ ||                          /1\     \        \x//                         \        \x// \      x   /       |            |                       /1\   \        \x//       |                             /1\|     /       2   \ |     1 + cot (x)| |  |                       /1\   \        \x//       |               2       /1\|                                                                                 
- |(3*sin(x) + x*cos(x))*tan|-| - -------------------------------------- - ------------------------------------------------ + ---------------------------------------------------------------|*cos(x) - 3*|(x*cos(x) + sin(x))*tan|-| - --------------------|*cos(x) + 3*|(-2*cos(x) + x*sin(x))*tan|-| + ----------------------------------- - -----------------------------------|*sin(x) + x*sin (x)*tan|-|   3*\1 + cot (x)/*||(-2*cos(x) + x*sin(x))*tan|-| + ----------------------------------- - -----------------------------------|*cos(x) + 2*|(x*cos(x) + sin(x))*tan|-| - --------------------|*sin(x) + x*cos(x)*sin(x)*tan|-||   6*\1 + cot (x)/*|-1 + -----------|*|- |(x*cos(x) + sin(x))*tan|-| - --------------------|*cos(x) + x*sin (x)*tan|-||       /                               2                  3\                     
  |                         \x/                      2                                             3                                                          3                              |            \                       \x/            x          /            |                          \x/                     2                                     2                |                       \x/                   ||                          \x/                     2                                     2                |            \                       \x/            x          /                             \x/|                   |          2     | \  \                       \x/            x          /                       \x//       |                  /       2   \      /       2   \ |                     
  \                                                 x                                             x                                                          x                               /                                                                           \                                                 x                                     x                 /                                             \\                                                 x                                     x                 /                                                                                               /                   \       cot (x)  /                                                                                         |         2      5*\1 + cot (x)/    3*\1 + cot (x)/ |                  /1\
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------- + 2*x*|2 + 2*cot (x) - ---------------- + ----------------|*cos(x)*sin(x)*tan|-|
                                                                                                                                                                                                    cot(x)                                                                                                                                                                                                                                                                                                                    2                                                                                                                                                                        cot(x)                                                              |                       2                  4        |                  \x/
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           cot (x)                                                                                                                                                                                                                                         \                    cot (x)            cot (x)     /
2x(3(cot⁡2(x)+1)3cot⁡4(x)−5(cot⁡2(x)+1)2cot⁡2(x)+2cot⁡2(x)+2)sin⁡(x)cos⁡(x)tan⁡(1x)−6(cot⁡2(x)+1cot⁡2(x)−1)(xsin⁡2(x)tan⁡(1x)−((xcos⁡(x)+sin⁡(x))tan⁡(1x)−(tan⁡2(1x)+1)sin⁡(x)x)cos⁡(x))(cot⁡2(x)+1)cot⁡(x)−3(cot⁡2(x)+1)(xsin⁡(x)cos⁡(x)tan⁡(1x)+2((xcos⁡(x)+sin⁡(x))tan⁡(1x)−(tan⁡2(1x)+1)sin⁡(x)x)sin⁡(x)+((xsin⁡(x)−2cos⁡(x))tan⁡(1x)−2(1+tan⁡(1x)x)(tan⁡2(1x)+1)sin⁡(x)x2+2(xcos⁡(x)+sin⁡(x))(tan⁡2(1x)+1)x2)cos⁡(x))cot⁡2(x)+xsin⁡2(x)tan⁡(1x)−3((xcos⁡(x)+sin⁡(x))tan⁡(1x)−(tan⁡2(1x)+1)sin⁡(x)x)cos⁡(x)+3((xsin⁡(x)−2cos⁡(x))tan⁡(1x)−2(1+tan⁡(1x)x)(tan⁡2(1x)+1)sin⁡(x)x2+2(xcos⁡(x)+sin⁡(x))(tan⁡2(1x)+1)x2)sin⁡(x)−((xcos⁡(x)+3sin⁡(x))tan⁡(1x)−3(xsin⁡(x)−2cos⁡(x))(tan⁡2(1x)+1)x2−6(1+tan⁡(1x)x)(xcos⁡(x)+sin⁡(x))(tan⁡2(1x)+1)x3+2(tan⁡2(1x)+1)(3+6tan⁡(1x)x+tan⁡2(1x)+1x2+2tan⁡2(1x)x2)sin⁡(x)x3)cos⁡(x)cot⁡(x)2 x \left(\frac{3 \left(\cot^{2}{\left(x \right)} + 1\right)^{3}}{\cot^{4}{\left(x \right)}} - \frac{5 \left(\cot^{2}{\left(x \right)} + 1\right)^{2}}{\cot^{2}{\left(x \right)}} + 2 \cot^{2}{\left(x \right)} + 2\right) \sin{\left(x \right)} \cos{\left(x \right)} \tan{\left(\frac{1}{x} \right)} - \frac{6 \left(\frac{\cot^{2}{\left(x \right)} + 1}{\cot^{2}{\left(x \right)}} - 1\right) \left(x \sin^{2}{\left(x \right)} \tan{\left(\frac{1}{x} \right)} - \left(\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \tan{\left(\frac{1}{x} \right)} - \frac{\left(\tan^{2}{\left(\frac{1}{x} \right)} + 1\right) \sin{\left(x \right)}}{x}\right) \cos{\left(x \right)}\right) \left(\cot^{2}{\left(x \right)} + 1\right)}{\cot{\left(x \right)}} - \frac{3 \left(\cot^{2}{\left(x \right)} + 1\right) \left(x \sin{\left(x \right)} \cos{\left(x \right)} \tan{\left(\frac{1}{x} \right)} + 2 \left(\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \tan{\left(\frac{1}{x} \right)} - \frac{\left(\tan^{2}{\left(\frac{1}{x} \right)} + 1\right) \sin{\left(x \right)}}{x}\right) \sin{\left(x \right)} + \left(\left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \tan{\left(\frac{1}{x} \right)} - \frac{2 \left(1 + \frac{\tan{\left(\frac{1}{x} \right)}}{x}\right) \left(\tan^{2}{\left(\frac{1}{x} \right)} + 1\right) \sin{\left(x \right)}}{x^{2}} + \frac{2 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \left(\tan^{2}{\left(\frac{1}{x} \right)} + 1\right)}{x^{2}}\right) \cos{\left(x \right)}\right)}{\cot^{2}{\left(x \right)}} + \frac{x \sin^{2}{\left(x \right)} \tan{\left(\frac{1}{x} \right)} - 3 \left(\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \tan{\left(\frac{1}{x} \right)} - \frac{\left(\tan^{2}{\left(\frac{1}{x} \right)} + 1\right) \sin{\left(x \right)}}{x}\right) \cos{\left(x \right)} + 3 \left(\left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \tan{\left(\frac{1}{x} \right)} - \frac{2 \left(1 + \frac{\tan{\left(\frac{1}{x} \right)}}{x}\right) \left(\tan^{2}{\left(\frac{1}{x} \right)} + 1\right) \sin{\left(x \right)}}{x^{2}} + \frac{2 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \left(\tan^{2}{\left(\frac{1}{x} \right)} + 1\right)}{x^{2}}\right) \sin{\left(x \right)} - \left(\left(x \cos{\left(x \right)} + 3 \sin{\left(x \right)}\right) \tan{\left(\frac{1}{x} \right)} - \frac{3 \left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \left(\tan^{2}{\left(\frac{1}{x} \right)} + 1\right)}{x^{2}} - \frac{6 \left(1 + \frac{\tan{\left(\frac{1}{x} \right)}}{x}\right) \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \left(\tan^{2}{\left(\frac{1}{x} \right)} + 1\right)}{x^{3}} + \frac{2 \left(\tan^{2}{\left(\frac{1}{x} \right)} + 1\right) \left(3 + \frac{6 \tan{\left(\frac{1}{x} \right)}}{x} + \frac{\tan^{2}{\left(\frac{1}{x} \right)} + 1}{x^{2}} + \frac{2 \tan^{2}{\left(\frac{1}{x} \right)}}{x^{2}}\right) \sin{\left(x \right)}}{x^{3}}\right) \cos{\left(x \right)}}{\cot{\left(x \right)}}
Simplificar
Gráfico
Derivada de x*sin(x)*tg(1/x)*cos(x)/ctg(x)
    © Sr Examen – Калькулятор