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^{x+1})

Lösung

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

Lösung

x^{x + 1} (ln (x) + \frac{x + 1}{x})

Schritte zur Lösung

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

Wende Exponentenregel an:

a^{b} = e^{b l n (a)}

x^{x + 1} = e^{(x + 1) l n (x)}

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

Wende die Kettenregel an:

e^{(x + 1) l n (x)} \frac{d}{d x} ((x + 1) ln (x))

= e^{(x + 1) l n (x)} \frac{d}{d x} ((x + 1) ln (x))

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

= e^{(x + 1) l n (x)} (ln (x) + \frac{x + 1}{x})

e^{(x + 1) l n (x)} = x^{x + 1}

= x^{x + 1} (ln (x) + \frac{x + 1}{x})

Graph

Beliebte Beispiele

(dx)/(dy)=sin(x+y)

\frac{d x}{d y} = sin (x + y)

y^{^{'}} = - a y

derivative of x^ay^{1-a}

\frac{d}{d x} (x^{a} y^{1 - a})

steigung (1,-1),(6,-1)

s l o p e (1, - 1), (6, - 1)

integral from 6 to 8 of (92)/((x-6)^3)

\int_{6}^{8} \frac{92}{( x - 6 ) ^{3}} d x