Производная (sec(x))^x^2

Вы ввели

        / 2\
        \x /
(sec(x))    

$$\sec^{x^{2}}{\left (x \right )}$$

Подробное решение

1. Не могу найти шаги в поиске этой производной.

   Но производная

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

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Ответ:

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

Первая производная

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

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

Вторая производная

        / 2\                                                                                 
        \x / /                 2                           2    2 /       2   \             \
(sec(x))    *\2*log(sec(x)) + x *(2*log(sec(x)) + x*tan(x))  + x *\1 + tan (x)/ + 4*x*tan(x)/

$$\left(x^{2} \left(x \tan{\left (x \right )} + 2 \log{\left (\sec{\left (x \right )} \right )}\right)^{2} + x^{2} \left(\tan^{2}{\left (x \right )} + 1\right) + 4 x \tan{\left (x \right )} + 2 \log{\left (\sec{\left (x \right )} \right )}\right) \sec^{x^{2}}{\left (x \right )}$$

Третья производная

        / 2\                                                                                                                                                                             
        \x / /            3                           3       /       2   \      2 /       2   \                                         /                 2 /       2   \             \\
(sec(x))    *\6*tan(x) + x *(2*log(sec(x)) + x*tan(x))  + 6*x*\1 + tan (x)/ + 2*x *\1 + tan (x)/*tan(x) + 3*x*(2*log(sec(x)) + x*tan(x))*\2*log(sec(x)) + x *\1 + tan (x)/ + 4*x*tan(x)//

$$\left(x^{3} \left(x \tan{\left (x \right )} + 2 \log{\left (\sec{\left (x \right )} \right )}\right)^{3} + 2 x^{2} \left(\tan^{2}{\left (x \right )} + 1\right) \tan{\left (x \right )} + 3 x \left(x \tan{\left (x \right )} + 2 \log{\left (\sec{\left (x \right )} \right )}\right) \left(x^{2} \left(\tan^{2}{\left (x \right )} + 1\right) + 4 x \tan{\left (x \right )} + 2 \log{\left (\sec{\left (x \right )} \right )}\right) + 6 x \left(\tan^{2}{\left (x \right )} + 1\right) + 6 \tan{\left (x \right )}\right) \sec^{x^{2}}{\left (x \right )}$$