derivative f(x)= 1/4 x^8-1/2 x^6-x+2

解

導関数

f (x) = \frac{1}{4} x^{8} - \frac{1}{2} x^{6} - x + 2

2 x^{7} - 3 x^{5} - 1

解答ステップ

\frac{d}{d x} (\frac{1}{4} x^{8} - \frac{1}{2} x^{6} - x + 2)

簡素化

\frac{1}{4} x^{8} - \frac{1}{2} x^{6} - x + 2 : \frac{x ^{8}}{4} - \frac{x ^{6}}{2} - x + 2

= \frac{d}{d x} (\frac{x ^{8}}{4} - \frac{x ^{6}}{2} - x + 2)

和/差の法則を適用:

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

= \frac{d}{d x} (\frac{x ^{8}}{4}) - \frac{d}{d x} (\frac{x ^{6}}{2}) - \frac{d x}{d x} + \frac{d}{d x} (2)

\frac{d}{d x} (\frac{x ^{8}}{4}) = 2 x^{7}

\frac{d}{d x} (\frac{x ^{6}}{2}) = 3 x^{5}

\frac{d x}{d x} = 1

\frac{d}{d x} (2) = 0

= 2 x^{7} - 3 x^{5} - 1 + 0

簡素化

= 2 x^{7} - 3 x^{5} - 1