derivative of 3^{sqrt(x)}

Lösung

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

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\int_{0}^{1} \frac{5}{x ^{2} + 1} d x

\int (\frac{3}{x} + 2 e^{x}) d x

a re a x^{2}, 12 - x, [- 3, 4]

x \to - 0 lim (e^{\frac{1}{x}})

\frac{d}{d x} (c^{1} cos (x) + c^{2} sin (x))