derivative of 3/(2+tan(x))

解

\frac{d}{d x} (\frac{3}{2 + tan ( x )})

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

解答ステップ

\frac{d}{d x} (\frac{3}{2 + tan ( x )})

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

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

指数の規則を適用する:

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

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

連鎖法則を適用:

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

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

\frac{d}{d x} (2 + tan (x)) = sec^{2} (x)

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

簡素化

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

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