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 5x^2e^x

解

導関数

5 x^{2} e^{x}

解

5 (2 x e^{x} + e^{x} x^{2})

解答ステップ

\frac{d}{d x} (5 x^{2} e^{x})

定数を除去:

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

= 5 \frac{d}{d x} (x^{2} e^{x})

積の法則を適用:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{2}, g = e^{x}

= 5 (\frac{d}{d x} (x^{2}) e^{x} + \frac{d}{d x} (e^{x}) x^{2})

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

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

= 5 (2 x e^{x} + e^{x} x^{2})

グラフ

人気の例

integral from 0 to 1 of (2x+3)e^{-5x}

\int_{0}^{1} (2 x + 3) e^{- 5 x} d x

derivative of (e^x(x^5+3)/(x^{10)+9})

\frac{d}{d x} (\frac{e ^{x} ( x ^{5} + 3 )}{x ^{10} + 9})

inverselaplace s/(s^2+a^2)

in v erse l a pl a ce \frac{s}{s ^{2} + a ^{2}}

sum from n=0 to infinity of 4^n

n = 0 \sum \infty 4^{n}

integral from-infinity to-4 of 3/(x^4)

\int_{- \infty}^{- 4} \frac{3}{x ^{4}} d x