(\partial)/(\partial u)(warctan(uv))

解

\frac{\partial}{\partial u} (w arctan (uv))

\frac{w v}{u ^{2} v ^{2} + 1}

解答ステップ

\frac{\partial}{\partial u} (w arctan (uv))

w, v

を定数として扱う

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= w \frac{\partial}{\partial u} (arctan (uv))

連鎖法則を適用:

\frac{1}{( uv ) ^{2} + 1} \frac{\partial}{\partial u} (uv)

= \frac{1}{( uv ) ^{2} + 1} \frac{\partial}{\partial u} (uv)

\frac{\partial}{\partial u} (uv) = v

= w \frac{1}{( uv ) ^{2} + 1} v

簡素化

w \frac{1}{( uv ) ^{2} + 1} v : \frac{w v}{u ^{2} v ^{2} + 1}

= \frac{w v}{u ^{2} v ^{2} + 1}