(\partial)/(\partial x)(4sqrt(y^2+7x^2))

解

\frac{\partial}{\partial x} (4 y^{2} + 7 x^{2})

\frac{28 x}{y ^{2} + 7 x ^{2}}

解答ステップ

\frac{\partial}{\partial x} (4 y^{2} + 7 x^{2})

y

を定数として扱う

定数を除去:

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

= 4 \frac{\partial}{\partial x} (y^{2} + 7 x^{2})

連鎖法則を適用:

\frac{1}{2 y ^{2} + 7 x ^{2}} \frac{\partial}{\partial x} (y^{2} + 7 x^{2})

= \frac{1}{2 y ^{2} + 7 x ^{2}} \frac{\partial}{\partial x} (y^{2} + 7 x^{2})

\frac{\partial}{\partial x} (y^{2} + 7 x^{2}) = 14 x

= 4 \cdot \frac{1}{2 y ^{2} + 7 x ^{2}} \cdot 14 x

簡素化

4 \cdot \frac{1}{2 y ^{2} + 7 x ^{2}} \cdot 14 x : \frac{28 x}{y ^{2} + 7 x ^{2}}

= \frac{28 x}{y ^{2} + 7 x ^{2}}