derivative sqrt(x^2+6x+9)

解

導関数

x^{2} + 6 x + 9

\frac{x + 3}{x ^{2} + 6 x + 9}

解答ステップ

\frac{d}{d x} (x^{2} + 6 x + 9)

連鎖法則を適用:

\frac{1}{2 x ^{2} + 6 x + 9} \frac{d}{d x} (x^{2} + 6 x + 9)

= \frac{1}{2 x ^{2} + 6 x + 9} \frac{d}{d x} (x^{2} + 6 x + 9)

\frac{d}{d x} (x^{2} + 6 x + 9) = 2 x + 6

= \frac{1}{2 x ^{2} + 6 x + 9} (2 x + 6)

簡素化

\frac{1}{2 x ^{2} + 6 x + 9} (2 x + 6) : \frac{x + 3}{x ^{2} + 6 x + 9}

= \frac{x + 3}{x ^{2} + 6 x + 9}