(\partial)/(\partial x)(sqrt(10x+8y))

解

\frac{\partial}{\partial x} (10 x + 8 y)

\frac{5}{10 x + 8 y}

解答ステップ

\frac{\partial}{\partial x} (10 x + 8 y)

y

を定数として扱う

連鎖法則を適用:

\frac{1}{2 10 x + 8 y} \frac{\partial}{\partial x} (10 x + 8 y)

= \frac{1}{2 10 x + 8 y} \frac{\partial}{\partial x} (10 x + 8 y)

\frac{\partial}{\partial x} (10 x + 8 y) = 10

= \frac{1}{2 10 x + 8 y} \cdot 10

簡素化

\frac{1}{2 10 x + 8 y} \cdot 10 : \frac{5}{10 x + 8 y}

= \frac{5}{10 x + 8 y}