derivative of 1/4 x^4-2x^2

解

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

x^{3} - 4 x

解答ステップ

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

簡素化

\frac{1}{4} x^{4} - 2 x^{2} : \frac{x ^{4}}{4} - 2 x^{2}

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

和/差の法則を適用:

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

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

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

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

= x^{3} - 4 x