derivative f(x)=sqrt(x^2+6x-1)

解

導関数

f (x) = x^{2} + 6 x - 1

\frac{x + 3}{x ^{2} + 6 x - 1}

解答ステップ

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

連鎖法則を適用:

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

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

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

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

簡素化

\frac{1}{2 x ^{2} + 6 x - 1} (2 x + 6) : \frac{x + 3}{x ^{2} + 6 x - 1}

= \frac{x + 3}{x ^{2} + 6 x - 1}