derivative f(x)=sqrt(8x^2-x)

解

導関数

f (x) = 8 x^{2} - x

\frac{16 x - 1}{2 8 x ^{2} - x}

解答ステップ

\frac{d}{d x} (8 x^{2} - x)

連鎖法則を適用:

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

= \frac{1}{2 8 x ^{2} - x} \frac{d}{d x} (8 x^{2} - x)

\frac{d}{d x} (8 x^{2} - x) = 16 x - 1

= \frac{1}{2 8 x ^{2} - x} (16 x - 1)

簡素化

\frac{1}{2 8 x ^{2} - x} (16 x - 1) : \frac{16 x - 1}{2 8 x ^{2} - x}

= \frac{16 x - 1}{2 8 x ^{2} - x}