(\partial)/(\partial s)(-3sqrt(s^2+t^2))

解

\frac{\partial}{\partial s} (- 3 s^{2} + t^{2})

- \frac{3 s}{s ^{2} + t ^{2}}

解答ステップ

\frac{\partial}{\partial s} (- 3 s^{2} + t^{2})

t

を定数として扱う

定数を除去:

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

= - 3 \frac{\partial}{\partial s} (s^{2} + t^{2})

連鎖法則を適用:

\frac{1}{2 s ^{2} + t ^{2}} \frac{\partial}{\partial s} (s^{2} + t^{2})

= \frac{1}{2 s ^{2} + t ^{2}} \frac{\partial}{\partial s} (s^{2} + t^{2})

\frac{\partial}{\partial s} (s^{2} + t^{2}) = 2 s

= - 3 \cdot \frac{1}{2 s ^{2} + t ^{2}} \cdot 2 s

簡素化

- 3 \cdot \frac{1}{2 s ^{2} + t ^{2}} \cdot 2 s : - \frac{3 s}{s ^{2} + t ^{2}}

= - \frac{3 s}{s ^{2} + t ^{2}}