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Beliebt Rechnen >

derivative g(t)=sqrt(2)^t

Lösung

ableitung von

g (t) = 2^{t}

Lösung

\frac{1}{2} ln (2) e^{\frac{l n ( 2 ) t}{2}}

Schritte zur Lösung

\frac{d}{d t} ((2)^{t})

Vereinfache

(2)^{t} : 2^{\frac{t}{2}}

= \frac{d}{d t} (2^{\frac{t}{2}})

Wende Exponentenregel an:

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

2^{\frac{t}{2}} = e^{\frac{t}{2} l n (2)}

= \frac{d}{d t} (e^{\frac{t}{2} l n (2)})

Wende die Kettenregel an:

e^{\frac{t}{2} l n (2)} \frac{d}{d t} (\frac{t}{2} ln (2))

= e^{\frac{t}{2} l n (2)} \frac{d}{d t} (\frac{t}{2} ln (2))

\frac{d}{d t} (\frac{t}{2} ln (2)) = \frac{1}{2} ln (2)

= e^{\frac{t}{2} l n (2)} \frac{1}{2} ln (2)

Multipliziere Brüche:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1}{2} ln (2) e^{\frac{l n ( 2 ) t}{2}}

Graph

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