de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

derivative x^{5/2}e^x

Lösung

ableitung von

x^{\frac{5}{2}} e^{x}

Lösung

\frac{5 e ^{x} x ^{\frac{3}{2}}}{2} + e^{x} x^{\frac{5}{2}}

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x^{\frac{5}{2}}, g = e^{x}

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

\frac{d}{d x} (x^{\frac{5}{2}}) = \frac{5 x ^{\frac{3}{2}}}{2}

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

= \frac{5 x ^{\frac{3}{2}}}{2} e^{x} + e^{x} x^{\frac{5}{2}}

Multipliziere Brüche:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{5 e ^{x} x ^{\frac{3}{2}}}{2} + e^{x} x^{\frac{5}{2}}

Graph

Beliebte Beispiele

limit as x approaches 9+of 2/(x+9)

x \to 9 + lim (\frac{2}{x + 9})

derivative e^{x+2}+2

d er i v a t i v e e^{x + 2} + 2

integral of-7/5 x^{-12}

\int - \frac{7}{5} x^{- 12} d x

derivative of e^{cos(x}sin(x^2-x))

\frac{d}{d x} (e^{c o s (x)} sin (x^{2} - x))

integral of (3^2+x^{12})

\int (3^{2} + x^{12}) d x