derivative y=4x^2-13x-9/(x^4)

解

導関数

y = 4 x^{2} - 13 x - \frac{9}{x ^{4}}

8 x - 13 + \frac{36}{x ^{5}}

解答ステップ

\frac{d}{d x} (4 x^{2} - 13 x - \frac{9}{x ^{4}})

和/差の法則を適用:

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

= \frac{d}{d x} (4 x^{2}) - \frac{d}{d x} (13 x) - \frac{d}{d x} (\frac{9}{x ^{4}})

\frac{d}{d x} (4 x^{2}) = 8 x

\frac{d}{d x} (13 x) = 13

\frac{d}{d x} (\frac{9}{x ^{4}}) = - \frac{36}{x ^{5}}

= 8 x - 13 - (- \frac{36}{x ^{5}})

簡素化

= 8 x - 13 + \frac{36}{x ^{5}}