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Beliebt Rechnen >

derivative of 5^{x+1}

Lösung

\frac{d}{d x} (5^{x + 1})

Lösung

ln (5) \cdot 5^{x + 1}

Schritte zur Lösung

\frac{d}{d x} (5^{x + 1})

Wende Exponentenregel an:

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

5^{x + 1} = e^{(x + 1) l n (5)}

= \frac{d}{d x} (e^{(x + 1) l n (5)})

Wende die Kettenregel an:

e^{(x + 1) l n (5)} \frac{d}{d x} ((x + 1) ln (5))

= e^{(x + 1) l n (5)} \frac{d}{d x} ((x + 1) ln (5))

\frac{d}{d x} ((x + 1) ln (5)) = ln (5)

= e^{(x + 1) l n (5)} ln (5)

e^{(x + 1) l n (5)} = 5^{x + 1}

= ln (5) \cdot 5^{x + 1}

Graph

Beliebte Beispiele

t an g e n t - 3 x^{2}

derivative of 4/(4x+1)

\frac{d}{d x} (\frac{4}{4 x + 1})

integral of (4+8x)/(1+x^2)

\int \frac{4 + 8 x}{1 + x ^{2}} d x

integral of 9x^2+4x-3

\int 9 x^{2} + 4 x - 3 d x

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

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