derivative of 2^{3^{x^2}}

Lösung

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

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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