derivative f(x)=ln(sqrt(5x-7))

解

導関数

f (x) = ln (5 x - 7)

\frac{5}{2 ( 5 x - 7 )}

解答ステップ

\frac{d}{d x} (ln (5 x - 7))

連鎖法則を適用:

\frac{1}{5 x - 7} \frac{d}{d x} (5 x - 7)

= \frac{1}{5 x - 7} \frac{d}{d x} (5 x - 7)

\frac{d}{d x} (5 x - 7) = \frac{5}{2 5 x - 7}

= \frac{1}{5 x - 7} \cdot \frac{5}{2 5 x - 7}

簡素化

\frac{1}{5 x - 7} \cdot \frac{5}{2 5 x - 7} : \frac{5}{2 ( 5 x - 7 )}

= \frac{5}{2 ( 5 x - 7 )}