derivative f(x)= 1/(3(x)^2+2(x))

解

導関数

f (x) = \frac{1}{3 ( x ) ^{2} + 2 ( x )}

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

解答ステップ

\frac{d}{d x} (\frac{1}{3 x ^{2} + 2 x})

指数の規則を適用する:

\frac{1}{a} = a^{- 1}

= \frac{d}{d x} ((3 x^{2} + 2 x)^{- 1})

連鎖法則を適用:

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

= - \frac{1}{( 3 x ^{2} + 2 x ) ^{2}} \frac{d}{d x} (3 x^{2} + 2 x)

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

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

簡素化

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

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