derivative of (2x^7+5x^3-1/4)

解

\frac{d}{d x} (\frac{2 x ^{7} + 5 x ^{3} - 1}{4})

\frac{1}{4} (14 x^{6} + 15 x^{2})

解答ステップ

\frac{d}{d x} (\frac{2 x ^{7} + 5 x ^{3} - 1}{4})

定数を除去:

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

= \frac{1}{4} \frac{d}{d x} (2 x^{7} + 5 x^{3} - 1)

和/差の法則を適用:

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

= \frac{1}{4} (\frac{d}{d x} (2 x^{7}) + \frac{d}{d x} (5 x^{3}) - \frac{d}{d x} (1))

\frac{d}{d x} (2 x^{7}) = 14 x^{6}

\frac{d}{d x} (5 x^{3}) = 15 x^{2}

\frac{d}{d x} (1) = 0

= \frac{1}{4} (14 x^{6} + 15 x^{2} - 0)

簡素化

= \frac{1}{4} (14 x^{6} + 15 x^{2})