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Beliebt Rechnen >

derivative of 3^{x+1}

Lösung

\frac{d}{d x} (3^{x + 1})

Lösung

ln (3) \cdot 3^{x + 1}

Schritte zur Lösung

\frac{d}{d x} (3^{x + 1})

Wende Exponentenregel an:

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

3^{x + 1} = e^{(x + 1) l n (3)}

= \frac{d}{d x} (e^{(x + 1) l n (3)})

Wende die Kettenregel an:

e^{(x + 1) l n (3)} \frac{d}{d x} ((x + 1) ln (3))

= e^{(x + 1) l n (3)} \frac{d}{d x} ((x + 1) ln (3))

\frac{d}{d x} ((x + 1) ln (3)) = ln (3)

= e^{(x + 1) l n (3)} ln (3)

e^{(x + 1) l n (3)} = 3^{x + 1}

= ln (3) \cdot 3^{x + 1}

Graph

Beliebte Beispiele

integral from 4 to 5 of (x^3-pix^2)

\int_{4}^{5} (x^{3} - π x^{2}) d x

sum from n=0 to infinity of 2^{1/n}

n = 0 \sum \infty 2^{\frac{1}{n}}

derivative of 4x^3-52x^2+160x

\frac{d}{d x} (4 x^{3} - 52 x^{2} + 160 x)

\frac{d}{d z} (ln (z))

integral of 3x+7

\int 3 x + 7 d x