Производная (atan(u))^v

Вы ввели

    v   
atan (u)

$$\operatorname{atan}^{v}{\left (u \right )}$$

Подробное решение

1. $\frac{\partial}{\partial v} \operatorname{atan}^{v}{\left (u \right )} = \log{\left (\operatorname{atan}{\left (u \right )} \right )} \operatorname{atan}^{v}{\left (u \right )}$

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Ответ:

$\log{\left (\operatorname{atan}{\left (u \right )} \right )} \operatorname{atan}^{v}{\left (u \right )}$

Первая производная

    v                
atan (u)*log(atan(u))

$$\log{\left (\operatorname{atan}{\left (u \right )} \right )} \operatorname{atan}^{v}{\left (u \right )}$$

Вторая производная

    v       2         
atan (u)*log (atan(u))

$$\log^{2}{\left (\operatorname{atan}{\left (u \right )} \right )} \operatorname{atan}^{v}{\left (u \right )}$$

Третья производная

    v       3         
atan (u)*log (atan(u))

$$\log^{3}{\left (\operatorname{atan}{\left (u \right )} \right )} \operatorname{atan}^{v}{\left (u \right )}$$