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 ((-e^x))/(x+1)

解

導関数

\frac{( - e ^{x} )}{x + 1}

解

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

解答ステップ

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

簡素化

\frac{- e ^{x}}{x + 1} : - \frac{e ^{x}}{x + 1}

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

定数を除去:

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

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

商の法則を適用:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{d}{d x} (e^{x}) = e^{x}

\frac{d}{d x} (x + 1) = 1

= - \frac{e ^{x} ( x + 1 ) - 1 \cdot e ^{x}}{( x + 1 ) ^{2}}

簡素化

- \frac{e ^{x} ( x + 1 ) - 1 \cdot e ^{x}}{( x + 1 ) ^{2}} : - \frac{e ^{x} x}{( x + 1 ) ^{2}}

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

グラフ

人気の例

integral of (13)/((x-2)(x^2+9))

\int \frac{13}{( x - 2 ) ( x ^{2} + 9 )} d x

limit as x approaches 7+of 1/(x+7)

x \to 7 + lim (\frac{1}{x + 7})

limit as x approaches 0 of (2sin(3x))/(5x)

x \to 0 lim (\frac{2 sin ( 3 x )}{5 x})

(\partial)/(\partial x)(9x^7cos(y^4))

\frac{\partial}{\partial x} (9 x^{7} cos (y^{4}))

y^{''}-3y^'-4y=e^{3t}

y^{^{''}} - 3 y^{^{'}} - 4 y = e^{3 t}