derivative 3^{x^3}

Lösung

ableitung von

3^{x^{3}}

ln (3) \cdot 3^{x^{3} + 1} x^{2}

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

e^{x^{3} l n (3)} \cdot 3 ln (3) x^{2} : ln (3) \cdot 3^{x^{3} + 1} x^{2}

= ln (3) \cdot 3^{x^{3} + 1} x^{2}

d er i v a t i v e p (x) = (x - 3)^{3} - (x - 2)^{2} + 31

\int_{\frac{1}{2}}^{1} \frac{x + 4}{x ^{2} + x} d x

\int_{0}^{1} \int 1 d x d y

x \to 4 lim (x + 2)

\int_{1}^{8} π (x - 1) d x