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

解

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

\frac{1}{9} (12 x - 4 x^{3})

解答ステップ

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

定数を除去:

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

= \frac{1}{9} \frac{d}{d x} (6 x^{2} - x^{4})

和/差の法則を適用:

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

= \frac{1}{9} (\frac{d}{d x} (6 x^{2}) - \frac{d}{d x} (x^{4}))

\frac{d}{d x} (6 x^{2}) = 12 x

\frac{d}{d x} (x^{4}) = 4 x^{3}

= \frac{1}{9} (12 x - 4 x^{3})