Производная (sec(x))^x

Вы ввели

   x   
sec (x)

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

Подробное решение

1. Не могу найти шаги в поиске этой производной.

   Но производная

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

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Ответ:

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

Первая производная

   x                            
sec (x)*(x*tan(x) + log(sec(x)))

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

Вторая производная

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

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

Третья производная

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

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