derivative of 1/(3x^2-5/(2x)+8x-6)

解

\frac{d}{d x} (\frac{1}{3 x ^{2}} - \frac{5}{2 x} + 8 x - 6)

\frac{5}{2 x ^{2}} - \frac{2}{3 x ^{3}} + 8

解答ステップ

\frac{d}{d x} (\frac{1}{3 x ^{2}} - \frac{5}{2 x} + 8 x - 6)

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (\frac{1}{3 x ^{2}}) - \frac{d}{d x} (\frac{5}{2 x}) + \frac{d}{d x} (8 x) - \frac{d}{d x} (6)

\frac{d}{d x} (\frac{1}{3 x ^{2}}) = - \frac{2}{3 x ^{3}}

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

\frac{d}{d x} (8 x) = 8

\frac{d}{d x} (6) = 0

= - \frac{2}{3 x ^{3}} - (- \frac{5}{2 x ^{2}}) + 8 - 0

簡素化

= \frac{5}{2 x ^{2}} - \frac{2}{3 x ^{3}} + 8