(\partial)/(\partial u)(sqrt(5u^2+8v^2))

解

\frac{\partial}{\partial u} (5 u^{2} + 8 v^{2})

\frac{5 u}{5 u ^{2} + 8 v ^{2}}

解答ステップ

\frac{\partial}{\partial u} (5 u^{2} + 8 v^{2})

v

を定数として扱う

連鎖法則を適用:

\frac{1}{2 5 u ^{2} + 8 v ^{2}} \frac{\partial}{\partial u} (5 u^{2} + 8 v^{2})

= \frac{1}{2 5 u ^{2} + 8 v ^{2}} \frac{\partial}{\partial u} (5 u^{2} + 8 v^{2})

\frac{\partial}{\partial u} (5 u^{2} + 8 v^{2}) = 10 u

= \frac{1}{2 5 u ^{2} + 8 v ^{2}} \cdot 10 u

簡素化

\frac{1}{2 5 u ^{2} + 8 v ^{2}} \cdot 10 u : \frac{5 u}{5 u ^{2} + 8 v ^{2}}

= \frac{5 u}{5 u ^{2} + 8 v ^{2}}