Derivada de x^secx

Ha introducido [src]

 sec(x)
x

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

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)                       \
x      *|------ + log(x)*sec(x)*tan(x)|
        \  x                          /

x^{\sec{\left(x \right)}} \left(\log{\left(x \right)} \tan{\left(x \right)} \sec{\left(x \right)} + \frac{\sec{\left(x \right)}}{x}\right)

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Segunda derivada [src]

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

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

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Tercera derivada [src]

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

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

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Gráfico

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Expresiones idénticas

Derivada de x^secx

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Solución