derivative of 4/5 ln((9x^2-6^7))

解

\frac{d}{d x} (\frac{4}{5} ln ((9 x^{2} - 6)^{7}))

\frac{168 x}{5 ( 3 x ^{2} - 2 )}

解答ステップ

\frac{d}{d x} (\frac{4}{5} ln ((9 x^{2} - 6)^{7}))

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{4}{5} \frac{d}{d x} (ln ((9 x^{2} - 6)^{7}))

連鎖法則を適用:

\frac{1}{( 9 x ^{2} - 6 ) ^{7}} \frac{d}{d x} ((9 x^{2} - 6)^{7})

= \frac{1}{( 9 x ^{2} - 6 ) ^{7}} \frac{d}{d x} ((9 x^{2} - 6)^{7})

\frac{d}{d x} ((9 x^{2} - 6)^{7}) = 126 x (9 x^{2} - 6)^{6}

= \frac{4}{5} \cdot \frac{1}{( 9 x ^{2} - 6 ) ^{7}} \cdot 126 x (9 x^{2} - 6)^{6}

簡素化

\frac{4}{5} \cdot \frac{1}{( 9 x ^{2} - 6 ) ^{7}} \cdot 126 x (9 x^{2} - 6)^{6} : \frac{168 x}{5 ( 3 x ^{2} - 2 )}

= \frac{168 x}{5 ( 3 x ^{2} - 2 )}