(\partial)/(\partial x)(sqrt(5x^2+5y^2))

解

\frac{\partial}{\partial x} (5 x^{2} + 5 y^{2})

\frac{5 x}{5 x ^{2} + 5 y ^{2}}

解答ステップ

\frac{\partial}{\partial x} (5 x^{2} + 5 y^{2})

y

を定数として扱う

連鎖法則を適用:

\frac{1}{2 5 x ^{2} + 5 y ^{2}} \frac{\partial}{\partial x} (5 x^{2} + 5 y^{2})

= \frac{1}{2 5 x ^{2} + 5 y ^{2}} \frac{\partial}{\partial x} (5 x^{2} + 5 y^{2})

\frac{\partial}{\partial x} (5 x^{2} + 5 y^{2}) = 10 x

= \frac{1}{2 5 x ^{2} + 5 y ^{2}} \cdot 10 x

簡素化

\frac{1}{2 5 x ^{2} + 5 y ^{2}} \cdot 10 x : \frac{5 x}{5 x ^{2} + 5 y ^{2}}

= \frac{5 x}{5 x ^{2} + 5 y ^{2}}