(\partial)/(\partial x)(ln(ln(2x+2y)))

解

\frac{\partial}{\partial x} (ln (ln (2 x + 2 y)))

\frac{1}{ln ( 2 x + 2 y ) ( x + y )}

解答ステップ

\frac{\partial}{\partial x} (ln (ln (2 x + 2 y)))

y

を定数として扱う

連鎖法則を適用:

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

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

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

= \frac{1}{ln ( 2 x + 2 y )} \cdot \frac{1}{x + y}

簡素化

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

= \frac{1}{ln ( 2 x + 2 y ) ( x + y )}