Derivada de y=(cos)^sec(x)

Ha introducido [src]

   sec(x)   
cos      (x)

$$\cos^{\sec{\left(x \right)}}{\left(x \right)}$$

cos(x)^sec(x)

Solución detallada

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Perola derivada

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

Respuesta:

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

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

   sec(x)    /                            sec(x)*sin(x)\
cos      (x)*|log(cos(x))*sec(x)*tan(x) - -------------|
             \                                cos(x)   /

$$\left(\log{\left(\cos{\left(x \right)} \right)} \tan{\left(x \right)} \sec{\left(x \right)} - \frac{\sin{\left(x \right)} \sec{\left(x \right)}}{\cos{\left(x \right)}}\right) \cos^{\sec{\left(x \right)}}{\left(x \right)}$$

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Segunda derivada [src]

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

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

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Tercera derivada [src]

             /                                         3                                                 3           2               /       2   \               2                                             /       2                                                                       \                                            \       
   sec(x)    |            /                     sin(x)\     2         3                  2*sin(x)   2*sin (x)   3*tan (x)*sin(x)   3*\1 + tan (x)/*sin(x)   3*sin (x)*tan(x)     /                     sin(x)\ |    sin (x)      2                  /       2   \               2*sin(x)*tan(x)|            /       2   \                   |       
cos      (x)*|-3*tan(x) + |log(cos(x))*tan(x) - ------| *sec (x) + tan (x)*log(cos(x)) - -------- - --------- - ---------------- - ---------------------- - ---------------- - 3*|log(cos(x))*tan(x) - ------|*|1 + ------- - tan (x)*log(cos(x)) - \1 + tan (x)/*log(cos(x)) + ---------------|*sec(x) + 5*\1 + tan (x)/*log(cos(x))*tan(x)|*sec(x)
             |            \                     cos(x)/                                   cos(x)        3            cos(x)                cos(x)                  2             \                     cos(x)/ |       2                                                             cos(x)    |                                            |       
             \                                                                                       cos (x)                                                    cos (x)                                        \    cos (x)                                                                    /                                            /

$$\left(\left(\log{\left(\cos{\left(x \right)} \right)} \tan{\left(x \right)} - \frac{\sin{\left(x \right)}}{\cos{\left(x \right)}}\right)^{3} \sec^{2}{\left(x \right)} - 3 \left(\log{\left(\cos{\left(x \right)} \right)} \tan{\left(x \right)} - \frac{\sin{\left(x \right)}}{\cos{\left(x \right)}}\right) \left(- \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(\cos{\left(x \right)} \right)} - \log{\left(\cos{\left(x \right)} \right)} \tan^{2}{\left(x \right)} + \frac{\sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} + \frac{2 \sin{\left(x \right)} \tan{\left(x \right)}}{\cos{\left(x \right)}} + 1\right) \sec{\left(x \right)} + 5 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(\cos{\left(x \right)} \right)} \tan{\left(x \right)} - \frac{3 \left(\tan^{2}{\left(x \right)} + 1\right) \sin{\left(x \right)}}{\cos{\left(x \right)}} + \log{\left(\cos{\left(x \right)} \right)} \tan^{3}{\left(x \right)} - \frac{2 \sin^{3}{\left(x \right)}}{\cos^{3}{\left(x \right)}} - \frac{3 \sin^{2}{\left(x \right)} \tan{\left(x \right)}}{\cos^{2}{\left(x \right)}} - \frac{3 \sin{\left(x \right)} \tan^{2}{\left(x \right)}}{\cos{\left(x \right)}} - \frac{2 \sin{\left(x \right)}}{\cos{\left(x \right)}} - 3 \tan{\left(x \right)}\right) \cos^{\sec{\left(x \right)}}{\left(x \right)} \sec{\left(x \right)}$$

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Gráfico

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Derivada de y=(cos)^sec(x)

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