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+1^{2x})

Lösung

\frac{d}{d x} ((x + 1)^{2 x})

Lösung

2 (ln (x + 1) + \frac{x}{x + 1}) (x + 1)^{2 x}

Schritte zur Lösung

\frac{d}{d x} ((x + 1)^{2 x})

Wende Exponentenregel an:

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

(x + 1)^{2 x} = e^{2 x l n (x + 1)}

= \frac{d}{d x} (e^{2 x l n (x + 1)})

Wende die Kettenregel an:

e^{2 x l n (x + 1)} \frac{d}{d x} (2 x ln (x + 1))

= e^{2 x l n (x + 1)} \frac{d}{d x} (2 x ln (x + 1))

\frac{d}{d x} (2 x ln (x + 1)) = 2 (ln (x + 1) + \frac{x}{x + 1})

= e^{2 x l n (x + 1)} \cdot 2 (ln (x + 1) + \frac{x}{x + 1})

e^{2 x l n (x + 1)} = (x + 1)^{2 x}

= 2 (ln (x + 1) + \frac{x}{x + 1}) (x + 1)^{2 x}

Graph

Beliebte Beispiele

derivative of (x^2-3x/2)

\frac{d}{d x} (\frac{x ^{2} - 3 x}{2})

tangent f(x)=3x^2-x^3,\at x=1

t an g e n t f (x) = 3 x^{2} - x^{3}, at x = 1

derivative of-3sin(x-2)

\frac{d}{d x} (- 3 sin (x) - 2)

derivative of x-2ln(x)

\frac{d}{d x} (x - 2 ln (x))

tangent f(x)=11+9x-x^3,\at x=1

t an g e n t f (x) = 11 + 9 x - x^{3}, at x = 1