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Beliebt Rechnen >

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

Lösung

ableitung von

3^{2^{x^{2}}}

Lösung

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

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

Wende die Kettenregel an:

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

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

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

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

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

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

Graph

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