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y=e^sinx^+secx
Derivada de la función/ e^sinx/ y=e^sinx^+secx

Derivada de y=e^sinx^+secx

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
    sec(x)   
 sin      (x)
E
esin⁡sec⁡(x)(x)e^{\sin^{\sec{\left(x \right)}}{\left(x \right)}} 
E^(sin(x)^sec(x))
Solución detallada

  1. Sustituimos u=sin⁡sec⁡(x)(x)u = \sin^{\sec{\left(x \right)}}{\left(x \right)}.

  2. Derivado eue^{u} es.

  3. Luego se aplica una cadena de reglas. Multiplicamos por ddxsin⁡sec⁡(x)(x)\frac{d}{d x} \sin^{\sec{\left(x \right)}}{\left(x \right)}:

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

      Perola derivada

      (log⁡(sec⁡(x))+1)sec⁡sec⁡(x)(x)\left(\log{\left(\sec{\left(x \right)} \right)} + 1\right) \sec^{\sec{\left(x \right)}}{\left(x \right)}

    Como resultado de la secuencia de reglas:

    (log⁡(sec⁡(x))+1)esin⁡sec⁡(x)(x)sec⁡sec⁡(x)(x)\left(\log{\left(\sec{\left(x \right)} \right)} + 1\right) e^{\sin^{\sec{\left(x \right)}}{\left(x \right)}} \sec^{\sec{\left(x \right)}}{\left(x \right)}

Respuesta:

(log⁡(sec⁡(x))+1)esin⁡sec⁡(x)(x)sec⁡sec⁡(x)(x)\left(\log{\left(\sec{\left(x \right)} \right)} + 1\right) e^{\sin^{\sec{\left(x \right)}}{\left(x \right)}} \sec^{\sec{\left(x \right)}}{\left(x \right)}

Gráfica
02468-8-6-4-2-101002e46
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
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)                               /
(log⁡(sin⁡(x))tan⁡(x)sec⁡(x)+cos⁡(x)sec⁡(x)sin⁡(x))esin⁡sec⁡(x)(x)sin⁡sec⁡(x)(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)}
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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)                                                                       /
((log⁡(sin⁡(x))tan⁡(x)+cos⁡(x)sin⁡(x))2sin⁡sec⁡(x)(x)sec⁡(x)+(log⁡(sin⁡(x))tan⁡(x)+cos⁡(x)sin⁡(x))2sec⁡(x)+(tan⁡2(x)+1)log⁡(sin⁡(x))+log⁡(sin⁡(x))tan⁡2(x)−1+2cos⁡(x)tan⁡(x)sin⁡(x)−cos⁡2(x)sin⁡2(x))esin⁡sec⁡(x)(x)sin⁡sec⁡(x)(x)sec⁡(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)}
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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)                  /       /
((log⁡(sin⁡(x))tan⁡(x)+cos⁡(x)sin⁡(x))3sin⁡2sec⁡(x)(x)sec⁡2(x)+3(log⁡(sin⁡(x))tan⁡(x)+cos⁡(x)sin⁡(x))3sin⁡sec⁡(x)(x)sec⁡2(x)+(log⁡(sin⁡(x))tan⁡(x)+cos⁡(x)sin⁡(x))3sec⁡2(x)+3(log⁡(sin⁡(x))tan⁡(x)+cos⁡(x)sin⁡(x))((tan⁡2(x)+1)log⁡(sin⁡(x))+log⁡(sin⁡(x))tan⁡2(x)−1+2cos⁡(x)tan⁡(x)sin⁡(x)−cos⁡2(x)sin⁡2(x))sin⁡sec⁡(x)(x)sec⁡(x)+3(log⁡(sin⁡(x))tan⁡(x)+cos⁡(x)sin⁡(x))((tan⁡2(x)+1)log⁡(sin⁡(x))+log⁡(sin⁡(x))tan⁡2(x)−1+2cos⁡(x)tan⁡(x)sin⁡(x)−cos⁡2(x)sin⁡2(x))sec⁡(x)+5(tan⁡2(x)+1)log⁡(sin⁡(x))tan⁡(x)+3(tan⁡2(x)+1)cos⁡(x)sin⁡(x)+log⁡(sin⁡(x))tan⁡3(x)−3tan⁡(x)+3cos⁡(x)tan⁡2(x)sin⁡(x)+2cos⁡(x)sin⁡(x)−3cos⁡2(x)tan⁡(x)sin⁡2(x)+2cos⁡3(x)sin⁡3(x))esin⁡sec⁡(x)(x)sin⁡sec⁡(x)(x)sec⁡(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)}
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Gráfico
Derivada de y=e^sinx^+secx
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