derivative of 8x^4-24x^2+r-1

解

\frac{d}{d x} (8 x^{4} - 24 x^{2} + r (x) - 1)

32 x^{3} - 48 x + \frac{d r}{d x}

解答ステップ

\frac{d}{d x} (8 x^{4} - 24 x^{2} + r - 1)

和/差の法則を適用:

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

= \frac{d}{d x} (8 x^{4}) - \frac{d}{d x} (24 x^{2}) + \frac{d r}{d x} - \frac{d}{d x} (1)

\frac{d}{d x} (8 x^{4}) = 32 x^{3}

\frac{d}{d x} (24 x^{2}) = 48 x

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

= 32 x^{3} - 48 x + \frac{d r}{d x} - 0

簡素化

= 32 x^{3} - 48 x + \frac{d r}{d x}