derivative of x^{4/5}(x-8^2)

解

\frac{d}{d x} (x^{\frac{4}{5}} (x - 8)^{2})

\frac{14 x ^{2} - 144 x + 256}{5 x ^{\frac{1}{5}}}

解答ステップ

\frac{d}{d x} (x^{\frac{4}{5}} (x - 8)^{2})

積の法則を適用:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{\frac{4}{5}}, g = (x - 8)^{2}

= \frac{d}{d x} (x^{\frac{4}{5}}) (x - 8)^{2} + \frac{d}{d x} ((x - 8)^{2}) x^{\frac{4}{5}}

\frac{d}{d x} (x^{\frac{4}{5}}) = \frac{4}{5 x ^{\frac{1}{5}}}

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

= \frac{4}{5 x ^{\frac{1}{5}}} (x - 8)^{2} + 2 (x - 8) x^{\frac{4}{5}}

簡素化

\frac{4}{5 x ^{\frac{1}{5}}} (x - 8)^{2} + 2 (x - 8) x^{\frac{4}{5}} : \frac{14 x ^{2} - 144 x + 256}{5 x ^{\frac{1}{5}}}

= \frac{14 x ^{2} - 144 x + 256}{5 x ^{\frac{1}{5}}}