(\partial)/(\partial x)(ln(sqrt(3x)+5y))

解

\frac{\partial}{\partial x} (ln (3 x + 5 y))

\frac{3}{2 x ( 3 x + 5 y )}

解答ステップ

\frac{\partial}{\partial x} (ln (3 x + 5 y))

簡素化

ln (3 x + 5 y) : ln (3 x + 5 y)

= \frac{\partial}{\partial x} (ln (3 x + 5 y))

y

を定数として扱う

連鎖法則を適用:

\frac{1}{3 x + 5 y} \frac{\partial}{\partial x} (3 x + 5 y)

= \frac{1}{3 x + 5 y} \frac{\partial}{\partial x} (3 x + 5 y)

\frac{\partial}{\partial x} (3 x + 5 y) = \frac{3}{2 x}

= \frac{1}{3 x + 5 y} \cdot \frac{3}{2 x}

簡素化

\frac{1}{3 x + 5 y} \cdot \frac{3}{2 x} : \frac{3}{2 x ( 3 x + 5 y )}

= \frac{3}{2 x ( 3 x + 5 y )}