(\partial)/(\partial L)(-sqrt(2{K)^2+L^2})

解

\frac{\partial}{\partial L} (- 2 K^{2} + L^{2})

- \frac{L}{2 K ^{2} + L ^{2}}

解答ステップ

\frac{\partial}{\partial L} (- 2 K^{2} + L^{2})

定数を除去:

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

= - \frac{\partial}{\partial L} (2 K^{2} + L^{2})

連鎖法則を適用:

\frac{1}{2 2 K ^{2} + L ^{2}} \frac{\partial}{\partial L} (2 K^{2} + L^{2})

= \frac{1}{2 2 K ^{2} + L ^{2}} \frac{\partial}{\partial L} (2 K^{2} + L^{2})

\frac{\partial}{\partial L} (2 K^{2} + L^{2}) = 2 L

= - \frac{1}{2 2 K ^{2} + L ^{2}} \cdot 2 L

簡素化

- \frac{1}{2 2 K ^{2} + L ^{2}} \cdot 2 L : - \frac{L}{2 K ^{2} + L ^{2}}

= - \frac{L}{2 K ^{2} + L ^{2}}