Sr Examen

Otras calculadoras

y=(tg^3)*2x*(cos^2)*2x

  • ¿Cómo usar?

  • Derivada de:
  • Derivada de -17x^2 Derivada de -17x^2
  • Derivada de x^-4/5 Derivada de x^-4/5
  • Derivada de x^2*5^x Derivada de x^2*5^x
  • Derivada de x/(1+e^x) Derivada de x/(1+e^x)

  • Expresiones idénticas

  • y=(tg^ tres)* dos x*(cos^2)*2x
  • y es igual a (tg al cubo ) multiplicar por 2x multiplicar por ( coseno de al cuadrado ) multiplicar por 2x
  • y es igual a (tg en el grado tres) multiplicar por dos x multiplicar por ( coseno de al cuadrado ) multiplicar por 2x
  • y=(tg3)*2x*(cos2)*2x
  • y=tg3*2x*cos2*2x
  • y=(tg³)*2x*(cos²)*2x
  • y=(tg en el grado 3)*2x*(cos en el grado 2)*2x
  • y=(tg^3)2x(cos^2)2x
  • y=(tg3)2x(cos2)2x
  • y=tg32xcos22x
  • y=tg^32xcos^22x
Derivada de la función/ cos^2/ y=(tg^3)*2x*(cos^2)*2x

Derivada de y=(tg^3)*2x*(cos^2)*2x

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
   3           2       
tan (x)*2*x*cos (x)*2*x
x2x2tan⁡3(x)cos⁡2(x)x 2 x 2 \tan^{3}{\left(x \right)} \cos^{2}{\left(x \right)} 
((((tan(x)^3*2)*x)*cos(x)^2)*2)*x
Solución detallada

  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)=2x2tan⁡3(x)cos⁡2(x)f{\left(x \right)} = 2 x 2 \tan^{3}{\left(x \right)} \cos^{2}{\left(x \right)}; 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. La derivada del producto de una constante por función es igual al producto de esta constante por la derivada de esta función.

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

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

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

          1. Según el principio, aplicamos: xx tenemos 11

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

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

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

          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:

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

          h(x)=tan⁡3(x)h{\left(x \right)} = \tan^{3}{\left(x \right)}; calculamos ddxh(x)\frac{d}{d x} h{\left(x \right)}:

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

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

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

            1. Reescribimos las funciones para diferenciar:

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

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

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

              Ahora aplicamos la regla de la derivada de una divesión:

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

            Como resultado de la secuencia de reglas:

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

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

        Entonces, como resultado: 6x(sin⁡2(x)+cos⁡2(x))tan⁡2(x)−4xsin⁡(x)cos⁡(x)tan⁡3(x)+2cos⁡2(x)tan⁡3(x)6 x \left(\sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)}\right) \tan^{2}{\left(x \right)} - 4 x \sin{\left(x \right)} \cos{\left(x \right)} \tan^{3}{\left(x \right)} + 2 \cos^{2}{\left(x \right)} \tan^{3}{\left(x \right)}

      Entonces, como resultado: 12x(sin⁡2(x)+cos⁡2(x))tan⁡2(x)−8xsin⁡(x)cos⁡(x)tan⁡3(x)+4cos⁡2(x)tan⁡3(x)12 x \left(\sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)}\right) \tan^{2}{\left(x \right)} - 8 x \sin{\left(x \right)} \cos{\left(x \right)} \tan^{3}{\left(x \right)} + 4 \cos^{2}{\left(x \right)} \tan^{3}{\left(x \right)}

    g(x)=xg{\left(x \right)} = x; calculamos ddxg(x)\frac{d}{d x} g{\left(x \right)}:

    1. Según el principio, aplicamos: xx tenemos 11

    Como resultado de: x(12x(sin⁡2(x)+cos⁡2(x))tan⁡2(x)−8xsin⁡(x)cos⁡(x)tan⁡3(x)+4cos⁡2(x)tan⁡3(x))+2x2tan⁡3(x)cos⁡2(x)x \left(12 x \left(\sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)}\right) \tan^{2}{\left(x \right)} - 8 x \sin{\left(x \right)} \cos{\left(x \right)} \tan^{3}{\left(x \right)} + 4 \cos^{2}{\left(x \right)} \tan^{3}{\left(x \right)}\right) + 2 x 2 \tan^{3}{\left(x \right)} \cos^{2}{\left(x \right)}

  2. Simplificamos:

    4x(xcos⁡(2x)+2x+sin⁡(2x))tan⁡2(x)4 x \left(x \cos{\left(2 x \right)} + 2 x + \sin{\left(2 x \right)}\right) \tan^{2}{\left(x \right)}

Respuesta:

4x(xcos⁡(2x)+2x+sin⁡(2x))tan⁡2(x)4 x \left(x \cos{\left(2 x \right)} + 2 x + \sin{\left(2 x \right)}\right) \tan^{2}{\left(x \right)}

Gráfica
02468-8-6-4-2-1010-100000100000
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
  /     2    /   3               2    /         2   \\          3                 \      3           2     
x*\2*cos (x)*\tan (x)*2 + 2*x*tan (x)*\3 + 3*tan (x)// - 8*x*tan (x)*cos(x)*sin(x)/ + tan (x)*2*x*cos (x)*2
x(−8xsin⁡(x)cos⁡(x)tan⁡3(x)+2(2x(3tan⁡2(x)+3)tan⁡2(x)+2tan⁡3(x))cos⁡2(x))+2x2tan⁡3(x)cos⁡2(x)x \left(- 8 x \sin{\left(x \right)} \cos{\left(x \right)} \tan^{3}{\left(x \right)} + 2 \left(2 x \left(3 \tan^{2}{\left(x \right)} + 3\right) \tan^{2}{\left(x \right)} + 2 \tan^{3}{\left(x \right)}\right) \cos^{2}{\left(x \right)}\right) + 2 x 2 \tan^{3}{\left(x \right)} \cos^{2}{\left(x \right)}
Simplificar
Segunda derivada [src] 
  /  /     2    /   2         2   \        2    /       2   \ /  /         2   \         \     /    /       2   \         \                     \      2    /    /       2   \         \                 2                 \       
8*\x*\x*tan (x)*\sin (x) - cos (x)/ + 3*cos (x)*\1 + tan (x)/*\x*\1 + 2*tan (x)/ + tan(x)/ - 2*\3*x*\1 + tan (x)/ + tan(x)/*cos(x)*sin(x)*tan(x)/ + cos (x)*\3*x*\1 + tan (x)/ + tan(x)/*tan(x) - 2*x*tan (x)*cos(x)*sin(x)/*tan(x)
8(x(x(sin⁡2(x)−cos⁡2(x))tan⁡2(x)−2(3x(tan⁡2(x)+1)+tan⁡(x))sin⁡(x)cos⁡(x)tan⁡(x)+3(x(2tan⁡2(x)+1)+tan⁡(x))(tan⁡2(x)+1)cos⁡2(x))−2xsin⁡(x)cos⁡(x)tan⁡2(x)+(3x(tan⁡2(x)+1)+tan⁡(x))cos⁡2(x)tan⁡(x))tan⁡(x)8 \left(x \left(x \left(\sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right) \tan^{2}{\left(x \right)} - 2 \left(3 x \left(\tan^{2}{\left(x \right)} + 1\right) + \tan{\left(x \right)}\right) \sin{\left(x \right)} \cos{\left(x \right)} \tan{\left(x \right)} + 3 \left(x \left(2 \tan^{2}{\left(x \right)} + 1\right) + \tan{\left(x \right)}\right) \left(\tan^{2}{\left(x \right)} + 1\right) \cos^{2}{\left(x \right)}\right) - 2 x \sin{\left(x \right)} \cos{\left(x \right)} \tan^{2}{\left(x \right)} + \left(3 x \left(\tan^{2}{\left(x \right)} + 1\right) + \tan{\left(x \right)}\right) \cos^{2}{\left(x \right)} \tan{\left(x \right)}\right) \tan{\left(x \right)}
Simplificar
Tercera derivada [src] 
  /  /                        /  /             2                                      \                           \                                                                                                                                                              \                                                                                                                                                        \
  |  |     2    /       2   \ |  |/       2   \         4           2    /       2   \|     /         2   \       |        2    /   2         2   \ /    /       2   \         \          3                       /       2   \ /  /         2   \         \                     |     /     2    /   2         2   \        2    /       2   \ /  /         2   \         \     /    /       2   \         \                     \       |
8*\x*\3*cos (x)*\1 + tan (x)/*\x*\\1 + tan (x)/  + 2*tan (x) + 7*tan (x)*\1 + tan (x)// + 3*\1 + 2*tan (x)/*tan(x)/ + 3*tan (x)*\sin (x) - cos (x)/*\3*x*\1 + tan (x)/ + tan(x)/ + 4*x*tan (x)*cos(x)*sin(x) - 18*\1 + tan (x)/*\x*\1 + 2*tan (x)/ + tan(x)/*cos(x)*sin(x)*tan(x)/ + 3*\x*tan (x)*\sin (x) - cos (x)/ + 3*cos (x)*\1 + tan (x)/*\x*\1 + 2*tan (x)/ + tan(x)/ - 2*\3*x*\1 + tan (x)/ + tan(x)/*cos(x)*sin(x)*tan(x)/*tan(x)/
8(x(4xsin⁡(x)cos⁡(x)tan⁡3(x)+3(3x(tan⁡2(x)+1)+tan⁡(x))(sin⁡2(x)−cos⁡2(x))tan⁡2(x)−18(x(2tan⁡2(x)+1)+tan⁡(x))(tan⁡2(x)+1)sin⁡(x)cos⁡(x)tan⁡(x)+3(x((tan⁡2(x)+1)2+7(tan⁡2(x)+1)tan⁡2(x)+2tan⁡4(x))+3(2tan⁡2(x)+1)tan⁡(x))(tan⁡2(x)+1)cos⁡2(x))+3(x(sin⁡2(x)−cos⁡2(x))tan⁡2(x)−2(3x(tan⁡2(x)+1)+tan⁡(x))sin⁡(x)cos⁡(x)tan⁡(x)+3(x(2tan⁡2(x)+1)+tan⁡(x))(tan⁡2(x)+1)cos⁡2(x))tan⁡(x))8 \left(x \left(4 x \sin{\left(x \right)} \cos{\left(x \right)} \tan^{3}{\left(x \right)} + 3 \left(3 x \left(\tan^{2}{\left(x \right)} + 1\right) + \tan{\left(x \right)}\right) \left(\sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right) \tan^{2}{\left(x \right)} - 18 \left(x \left(2 \tan^{2}{\left(x \right)} + 1\right) + \tan{\left(x \right)}\right) \left(\tan^{2}{\left(x \right)} + 1\right) \sin{\left(x \right)} \cos{\left(x \right)} \tan{\left(x \right)} + 3 \left(x \left(\left(\tan^{2}{\left(x \right)} + 1\right)^{2} + 7 \left(\tan^{2}{\left(x \right)} + 1\right) \tan^{2}{\left(x \right)} + 2 \tan^{4}{\left(x \right)}\right) + 3 \left(2 \tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}\right) \left(\tan^{2}{\left(x \right)} + 1\right) \cos^{2}{\left(x \right)}\right) + 3 \left(x \left(\sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right) \tan^{2}{\left(x \right)} - 2 \left(3 x \left(\tan^{2}{\left(x \right)} + 1\right) + \tan{\left(x \right)}\right) \sin{\left(x \right)} \cos{\left(x \right)} \tan{\left(x \right)} + 3 \left(x \left(2 \tan^{2}{\left(x \right)} + 1\right) + \tan{\left(x \right)}\right) \left(\tan^{2}{\left(x \right)} + 1\right) \cos^{2}{\left(x \right)}\right) \tan{\left(x \right)}\right)
Simplificar
Gráfico
Derivada de y=(tg^3)*2x*(cos^2)*2x
    © Sr Examen – Калькулятор