Sr Examen

Derivada de y=e^sinx^+secx

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src]
    sec(x)   
 sin      (x)
E            
$$e^{\sin^{\sec{\left(x \right)}}{\left(x \right)}}$$
E^(sin(x)^sec(x))
Solución detallada
  1. Sustituimos .

  2. Derivado es.

  3. Luego se aplica una cadena de reglas. Multiplicamos por :

    1. No logro encontrar los pasos en la búsqueda de esta derivada.

      Perola derivada

    Como resultado de la secuencia de reglas:


Respuesta:

Gráfica
Primera derivada [src]
                                                             sec(x)   
   sec(x)    /cos(x)*sec(x)                            \  sin      (x)
sin      (x)*|------------- + log(sin(x))*sec(x)*tan(x)|*e            
             \    sin(x)                               /              
$$\left(\log{\left(\sin{\left(x \right)} \right)} \tan{\left(x \right)} \sec{\left(x \right)} + \frac{\cos{\left(x \right)} \sec{\left(x \right)}}{\sin{\left(x \right)}}\right) e^{\sin^{\sec{\left(x \right)}}{\left(x \right)}} \sin^{\sec{\left(x \right)}}{\left(x \right)}$$
Segunda derivada [src]
             /                                  2                                                               2                                   2                                      \     sec(x)          
   sec(x)    |     /cos(x)                     \              2                  /       2   \               cos (x)   /cos(x)                     \     sec(x)             2*cos(x)*tan(x)|  sin      (x)       
sin      (x)*|-1 + |------ + log(sin(x))*tan(x)| *sec(x) + tan (x)*log(sin(x)) + \1 + tan (x)/*log(sin(x)) - ------- + |------ + log(sin(x))*tan(x)| *sin      (x)*sec(x) + ---------------|*e            *sec(x)
             |     \sin(x)                     /                                                                2      \sin(x)                     /                             sin(x)    |                     
             \                                                                                               sin (x)                                                                       /                     
$$\left(\left(\log{\left(\sin{\left(x \right)} \right)} \tan{\left(x \right)} + \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}\right)^{2} \sin^{\sec{\left(x \right)}}{\left(x \right)} \sec{\left(x \right)} + \left(\log{\left(\sin{\left(x \right)} \right)} \tan{\left(x \right)} + \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}\right)^{2} \sec{\left(x \right)} + \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(\sin{\left(x \right)} \right)} + \log{\left(\sin{\left(x \right)} \right)} \tan^{2}{\left(x \right)} - 1 + \frac{2 \cos{\left(x \right)} \tan{\left(x \right)}}{\sin{\left(x \right)}} - \frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) e^{\sin^{\sec{\left(x \right)}}{\left(x \right)}} \sin^{\sec{\left(x \right)}}{\left(x \right)} \sec{\left(x \right)}$$
Tercera derivada [src]
             /                                         3                                      3                                              3                               2                                            3                             2               /       2   \                                          /                                                          2                     \                                                                                            /                                                          2                     \       \     sec(x)          
   sec(x)    |            /cos(x)                     \     2         3                  2*cos (x)   2*cos(x)   /cos(x)                     \     2       2*sec(x)      3*cos (x)*tan(x)     /cos(x)                     \     2       sec(x)      3*tan (x)*cos(x)   3*\1 + tan (x)/*cos(x)     /cos(x)                     \ |        2                  /       2   \               cos (x)   2*cos(x)*tan(x)|            /       2   \                           sec(x)    /cos(x)                     \ |        2                  /       2   \               cos (x)   2*cos(x)*tan(x)|       |  sin      (x)       
sin      (x)*|-3*tan(x) + |------ + log(sin(x))*tan(x)| *sec (x) + tan (x)*log(sin(x)) + --------- + -------- + |------ + log(sin(x))*tan(x)| *sec (x)*sin        (x) - ---------------- + 3*|------ + log(sin(x))*tan(x)| *sec (x)*sin      (x) + ---------------- + ---------------------- + 3*|------ + log(sin(x))*tan(x)|*|-1 + tan (x)*log(sin(x)) + \1 + tan (x)/*log(sin(x)) - ------- + ---------------|*sec(x) + 5*\1 + tan (x)/*log(sin(x))*tan(x) + 3*sin      (x)*|------ + log(sin(x))*tan(x)|*|-1 + tan (x)*log(sin(x)) + \1 + tan (x)/*log(sin(x)) - ------- + ---------------|*sec(x)|*e            *sec(x)
             |            \sin(x)                     /                                      3        sin(x)    \sin(x)                     /                                  2             \sin(x)                     /                              sin(x)                sin(x)             \sin(x)                     / |                                                          2           sin(x)    |                                                              \sin(x)                     / |                                                          2           sin(x)    |       |                     
             \                                                                            sin (x)                                                                           sin (x)                                                                                                                                            \                                                       sin (x)                  /                                                                                            \                                                       sin (x)                  /       /                     
$$\left(\left(\log{\left(\sin{\left(x \right)} \right)} \tan{\left(x \right)} + \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}\right)^{3} \sin^{2 \sec{\left(x \right)}}{\left(x \right)} \sec^{2}{\left(x \right)} + 3 \left(\log{\left(\sin{\left(x \right)} \right)} \tan{\left(x \right)} + \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}\right)^{3} \sin^{\sec{\left(x \right)}}{\left(x \right)} \sec^{2}{\left(x \right)} + \left(\log{\left(\sin{\left(x \right)} \right)} \tan{\left(x \right)} + \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}\right)^{3} \sec^{2}{\left(x \right)} + 3 \left(\log{\left(\sin{\left(x \right)} \right)} \tan{\left(x \right)} + \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}\right) \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(\sin{\left(x \right)} \right)} + \log{\left(\sin{\left(x \right)} \right)} \tan^{2}{\left(x \right)} - 1 + \frac{2 \cos{\left(x \right)} \tan{\left(x \right)}}{\sin{\left(x \right)}} - \frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) \sin^{\sec{\left(x \right)}}{\left(x \right)} \sec{\left(x \right)} + 3 \left(\log{\left(\sin{\left(x \right)} \right)} \tan{\left(x \right)} + \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}\right) \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(\sin{\left(x \right)} \right)} + \log{\left(\sin{\left(x \right)} \right)} \tan^{2}{\left(x \right)} - 1 + \frac{2 \cos{\left(x \right)} \tan{\left(x \right)}}{\sin{\left(x \right)}} - \frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) \sec{\left(x \right)} + 5 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(\sin{\left(x \right)} \right)} \tan{\left(x \right)} + \frac{3 \left(\tan^{2}{\left(x \right)} + 1\right) \cos{\left(x \right)}}{\sin{\left(x \right)}} + \log{\left(\sin{\left(x \right)} \right)} \tan^{3}{\left(x \right)} - 3 \tan{\left(x \right)} + \frac{3 \cos{\left(x \right)} \tan^{2}{\left(x \right)}}{\sin{\left(x \right)}} + \frac{2 \cos{\left(x \right)}}{\sin{\left(x \right)}} - \frac{3 \cos^{2}{\left(x \right)} \tan{\left(x \right)}}{\sin^{2}{\left(x \right)}} + \frac{2 \cos^{3}{\left(x \right)}}{\sin^{3}{\left(x \right)}}\right) e^{\sin^{\sec{\left(x \right)}}{\left(x \right)}} \sin^{\sec{\left(x \right)}}{\left(x \right)} \sec{\left(x \right)}$$
Gráfico
Derivada de y=e^sinx^+secx