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Beliebt Rechnen >

derivative g(x)=3^{(x/2)}

Lösung

ableitung von

g (x) = 3^{(\frac{x}{2})}

Lösung

\frac{1}{2} ln (3) e^{\frac{l n ( 3 ) x}{2}}

Schritte zur Lösung

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

Wende Exponentenregel an:

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

3^{\frac{x}{2}} = e^{\frac{x}{2} l n (3)}

= \frac{d}{d x} (e^{\frac{x}{2} l n (3)})

Wende die Kettenregel an:

e^{\frac{x}{2} l n (3)} \frac{d}{d x} (\frac{x}{2} ln (3))

= e^{\frac{x}{2} l n (3)} \frac{d}{d x} (\frac{x}{2} ln (3))

\frac{d}{d x} (\frac{x}{2} ln (3)) = \frac{1}{2} ln (3)

= e^{\frac{x}{2} l n (3)} \frac{1}{2} ln (3)

Multipliziere Brüche:

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

= \frac{1}{2} ln (3) e^{\frac{l n ( 3 ) x}{2}}

Graph

Beliebte Beispiele

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