de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

derivative of x^6e^{-x}

Lösung

\frac{d}{d x} (x^{6} e^{- x})

Lösung

6 e^{- x} x^{5} - e^{- x} x^{6}

Schritte zur Lösung

\frac{d}{d x} (x^{6} e^{- x})

Wende die Produktregel an:

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

f = x^{6}, g = e^{- x}

= \frac{d}{d x} (x^{6}) e^{- x} + \frac{d}{d x} (e^{- x}) x^{6}

\frac{d}{d x} (x^{6}) = 6 x^{5}

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

= 6 x^{5} e^{- x} + (- e^{- x}) x^{6}

Vereinfache

= 6 e^{- x} x^{5} - e^{- x} x^{6}

Graph

Beliebte Beispiele

t a y l or ln (x), 6

derivative of 8+3sin(x)

\frac{d}{d x} (8 + 3 sin (x))

integral from 0 to 1 of x^{1/2}

\int_{0}^{1} x^{\frac{1}{2}} d x

sum from n=1 to infinity of 1/(2^nn!)

n = 1 \sum \infty \frac{1}{2 ^{n} n !}

xy^'+y=37sqrt(x)

x y^{^{'}} + y = 37 x