derivative sqrt(ln(7x+9))

解

導関数

ln (7 x + 9)

\frac{7}{2 ln ( 7 x + 9 ) ( 7 x + 9 )}

解答ステップ

\frac{d}{d x} (ln (7 x + 9))

連鎖法則を適用:

\frac{1}{2 ln ( 7 x + 9 )} \frac{d}{d x} (ln (7 x + 9))

= \frac{1}{2 ln ( 7 x + 9 )} \frac{d}{d x} (ln (7 x + 9))

\frac{d}{d x} (ln (7 x + 9)) = \frac{7}{7 x + 9}

= \frac{1}{2 ln ( 7 x + 9 )} \cdot \frac{7}{7 x + 9}

簡素化

\frac{1}{2 ln ( 7 x + 9 )} \cdot \frac{7}{7 x + 9} : \frac{7}{2 ln ( 7 x + 9 ) ( 7 x + 9 )}

= \frac{7}{2 ln ( 7 x + 9 ) ( 7 x + 9 )}