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 log_{8}(x^2-3x)

解

導関数

lo g_{8} (x^{2} - 3 x)

解

\frac{2 x - 3}{3 ln ( 2 ) ( x ^{2} - 3 x )}

解答ステップ

\frac{d}{d x} (lo g_{8} (x^{2} - 3 x))

対数の規則を適用する:

lo g_{a} (b) = \frac{ln ( b )}{ln ( a )}

= \frac{d}{d x} (\frac{ln ( x ^{2} - 3 x )}{ln ( 8 )})

定数を除去:

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

= \frac{1}{ln ( 8 )} \frac{d}{d x} (ln (x^{2} - 3 x))

連鎖法則を適用:

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

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

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

= \frac{1}{ln ( 8 )} \cdot \frac{1}{x ^{2} - 3 x} (2 x - 3)

簡素化

\frac{1}{ln ( 8 )} \cdot \frac{1}{x ^{2} - 3 x} (2 x - 3) : \frac{2 x - 3}{3 ln ( 2 ) ( x ^{2} - 3 x )}

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

グラフ

人気の例

integral of (ln(x+1))

\int (ln (x + 1)) d x

integral of sin(y)cos(y)

\int sin (y) cos (y) d y

implicit (dy)/(dx),x=e^y

im pl i c i t \frac{d y}{d x}, x = e^{y}

integral of 5/(4+9t^2)

\int \frac{5}{4 + 9 t ^{2}} d t

y^3-(18x+6)+3xy^2y^'=0

y^{3} - (18 x + 6) + 3 x y^{2} y^{^{'}} = 0