derivative y=sqrt(7x^3-6x^2-8/x)

解

導関数

y = 7 x^{3} - 6 x^{2} - \frac{8}{x}

\frac{21 x ^{4} - 12 x ^{3} + 8}{2 x ^{\frac{3}{2}} 7 x ^{4} - 6 x ^{3} - 8}

解答ステップ

\frac{d}{d x} (7 x^{3} - 6 x^{2} - \frac{8}{x})

連鎖法則を適用:

\frac{1}{2 7 x ^{3} - 6 x ^{2} - \frac{8}{x}} \frac{d}{d x} (7 x^{3} - 6 x^{2} - \frac{8}{x})

= \frac{1}{2 7 x ^{3} - 6 x ^{2} - \frac{8}{x}} \frac{d}{d x} (7 x^{3} - 6 x^{2} - \frac{8}{x})

\frac{d}{d x} (7 x^{3} - 6 x^{2} - \frac{8}{x}) = 21 x^{2} - 12 x + \frac{8}{x ^{2}}

= \frac{1}{2 7 x ^{3} - 6 x ^{2} - \frac{8}{x}} (21 x^{2} - 12 x + \frac{8}{x ^{2}})

簡素化

\frac{1}{2 7 x ^{3} - 6 x ^{2} - \frac{8}{x}} (21 x^{2} - 12 x + \frac{8}{x ^{2}}) : \frac{21 x ^{4} - 12 x ^{3} + 8}{2 x ^{\frac{3}{2}} 7 x ^{4} - 6 x ^{3} - 8}

= \frac{21 x ^{4} - 12 x ^{3} + 8}{2 x ^{\frac{3}{2}} 7 x ^{4} - 6 x ^{3} - 8}