derivative of 43^{sqrt(x)}

Lösung

\frac{d}{d x} (4 3^{x})

\frac{ln ( 43 ) \cdot 4 3 ^{x}}{2 x}

Schritte zur Lösung

\frac{d}{d x} (4 3^{x})

Wende Exponentenregel an:

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

4 3^{x} = e^{x l n (43)}

= \frac{d}{d x} (e^{x l n (43)})

Wende die Kettenregel an:

e^{x l n (43)} \frac{d}{d x} (x ln (43))

= e^{x l n (43)} \frac{d}{d x} (x ln (43))

\frac{d}{d x} (x ln (43)) = \frac{ln ( 43 )}{2 x}

= e^{x l n (43)} \frac{ln ( 43 )}{2 x}

Vereinfache

e^{x l n (43)} \frac{ln ( 43 )}{2 x} : \frac{ln ( 43 ) \cdot 4 3 ^{x}}{2 x}

= \frac{ln ( 43 ) \cdot 4 3 ^{x}}{2 x}

\int 28 x^{3} - 18 x^{2} + 8 x d x

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