(\partial)/(\partial y)(sqrt(x^2+6xy+4y^2))

解

\frac{\partial}{\partial y} (x^{2} + 6 x y + 4 y^{2})

\frac{4 y + 3 x}{x ^{2} + 6 x y + 4 y ^{2}}

解答ステップ

\frac{\partial}{\partial y} (x^{2} + 6 x y + 4 y^{2})

x

を定数として扱う

連鎖法則を適用:

\frac{1}{2 x ^{2} + 6 x y + 4 y ^{2}} \frac{\partial}{\partial y} (x^{2} + 6 x y + 4 y^{2})

= \frac{1}{2 x ^{2} + 6 x y + 4 y ^{2}} \frac{\partial}{\partial y} (x^{2} + 6 x y + 4 y^{2})

\frac{\partial}{\partial y} (x^{2} + 6 x y + 4 y^{2}) = 8 y + 6 x

= \frac{1}{2 x ^{2} + 6 x y + 4 y ^{2}} (8 y + 6 x)

簡素化

\frac{1}{2 x ^{2} + 6 x y + 4 y ^{2}} (8 y + 6 x) : \frac{4 y + 3 x}{x ^{2} + 6 x y + 4 y ^{2}}

= \frac{4 y + 3 x}{x ^{2} + 6 x y + 4 y ^{2}}