Sr Examen

Lang:

Otras calculadoras

¿Cómo usar?
Derivada de:
Derivada de -4*e^(4*t)+3*log(4*t)
Derivada de 3/x²
Derivada de 4*tan(2*t)-3*cot(2*t)
Derivada de -3*x*cos(x)
Expresiones idénticas
x*sin(x)^tg(x)
x multiplicar por seno de (x) en el grado tg(x)
x*sin(x)tg(x)
x*sinxtgx
xsin(x)^tg(x)
xsin(x)tg(x)
xsinxtgx
xsinx^tgx
Expresiones semejantes
x*sinx^tg(x)

Derivada de la función/ x*sin/ tg(x)/ sin(x)/ x*sin(x)^tg(x)

Derivada de x*sin(x)^tg(x)

Solución

Ha introducido [src]

     tan(x)   
x*sin      (x)

$$x \sin^{\tan{\left(x \right)}}{\left(x \right)}$$

x*sin(x)^tan(x)

Solución detallada

Se aplica la regla de la derivada de una multiplicación:

$\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$

$f{\left(x \right)} = x$ ; calculamos $\frac{d}{d x} f{\left(x \right)}$ :
1. Según el principio, aplicamos: $x$ tenemos $1$
$g{\left(x \right)} = \sin^{\tan{\left(x \right)}}{\left(x \right)}$ ; calculamos $\frac{d}{d x} g{\left(x \right)}$ :
1. No logro encontrar los pasos en la búsqueda de esta derivada.
  
  Perola derivada
  
  $\left(\log{\left(\tan{\left(x \right)} \right)} + 1\right) \tan^{\tan{\left(x \right)}}{\left(x \right)}$
Como resultado de: $x \left(\log{\left(\tan{\left(x \right)} \right)} + 1\right) \tan^{\tan{\left(x \right)}}{\left(x \right)} + \sin^{\tan{\left(x \right)}}{\left(x \right)}$

Respuesta:

$x \left(\log{\left(\tan{\left(x \right)} \right)} + 1\right) \tan^{\tan{\left(x \right)}}{\left(x \right)} + \sin^{\tan{\left(x \right)}}{\left(x \right)}$

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

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

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

Simplificar

Segunda derivada [src]

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

Simplificar

Tercera derivada [src]

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

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

Simplificar

Gráfico

Otras calculadoras

¿Cómo usar?

Expresiones idénticas

Expresiones semejantes

Derivada de x*sin(x)^tg(x)

Gráfico:

Definida a trozos:

Solución