ja

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

人気のある微分積分 >

derivative f(x)= 6/(ln(x^2+4))

解

導関数

f (x) = \frac{6}{ln ( x ^{2} + 4 )}

解

- \frac{12 x}{ln ^{2} ( x ^{2} + 4 ) ( x ^{2} + 4 )}

解答ステップ

\frac{d}{d x} (\frac{6}{ln ( x ^{2} + 4 )})

定数を除去:

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

= 6 \frac{d}{d x} (\frac{1}{ln ( x ^{2} + 4 )})

指数の規則を適用する:

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

= 6 \frac{d}{d x} (ln^{- 1} (x^{2} + 4))

連鎖法則を適用:

- \frac{1}{( ln ( x ^{2} + 4 ) ) ^{2}} \frac{d}{d x} (ln (x^{2} + 4))

= - \frac{1}{( ln ( x ^{2} + 4 ) ) ^{2}} \frac{d}{d x} (ln (x^{2} + 4))

\frac{d}{d x} (ln (x^{2} + 4)) = \frac{2 x}{x ^{2} + 4}

= 6 (- \frac{1}{( ln ( x ^{2} + 4 ) ) ^{2}} \cdot \frac{2 x}{x ^{2} + 4})

簡素化

6 (- \frac{1}{ln ^{2} ( x ^{2} + 4 )} \cdot \frac{2 x}{x ^{2} + 4}) : - \frac{12 x}{ln ^{2} ( x ^{2} + 4 ) ( x ^{2} + 4 )}

= - \frac{12 x}{ln ^{2} ( x ^{2} + 4 ) ( x ^{2} + 4 )}

グラフ

人気の例

integral of (sin(44x))/(1+cos^2(44x))

\int \frac{sin ( 44 x )}{1 + cos ^{2} ( 44 x )} d x

integral of 2x(x^2+1)^{-7}

\int 2 x (x^{2} + 1)^{- 7} d x

面積 f(x)=x^2,[0,3]

a re a f (x) = x^{2}, [0, 3]

integral from-1 to 3 of (x^2+6x+3)

\int_{- 1}^{3} (x^{2} + 6 x + 3) d x

(d^3)/(dx^3)(x^4-10x^3)

\frac{d ^{3}}{d x ^{3}} (x^{4} - 10 x^{3})