de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

derivative of e^xx^2+4e^xx+2e^x

Lösung

\frac{d}{d x} (e^{x} x^{2} + 4 e^{x} x + 2 e^{x})

Lösung

e^{x} x^{2} + 6 e^{x} x + 6 e^{x}

Schritte zur Lösung

\frac{d}{d x} (e^{x} x^{2} + 4 e^{x} x + 2 e^{x})

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (e^{x} x^{2}) + \frac{d}{d x} (4 e^{x} x) + \frac{d}{d x} (2 e^{x})

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

\frac{d}{d x} (4 e^{x} x) = 4 (e^{x} x + e^{x})

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

= e^{x} x^{2} + 2 x e^{x} + 4 (e^{x} x + e^{x}) + 2 e^{x}

Vereinfache

e^{x} x^{2} + 2 x e^{x} + 4 (e^{x} x + e^{x}) + 2 e^{x} : e^{x} x^{2} + 6 e^{x} x + 6 e^{x}

= e^{x} x^{2} + 6 e^{x} x + 6 e^{x}

Graph

Beliebte Beispiele

integral of 7e^xsqrt(3+e^x)

\int 7 e^{x} 3 + e^{x} d x

integral of r^5

\int r^{5} d r

limit as x approaches 0 of cosh(x)

x \to 0 lim (cosh (x))

(dy)/(dx)=(x/(sqrt(1-6x^2)))

\frac{d y}{d x} = (\frac{x}{1 - 6 x ^{2}})

integral of (10x^3+7/(x^2)-x)

\int (10 x^{3} + \frac{7}{x ^{2}} - x) d x