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Beliebt Rechnen >

derivative 2^{x^2-3}

Lösung

ableitung von

2^{x^{2} - 3}

Lösung

ln (2) \cdot 2^{x^{2} - 2} x

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

= ln (2) \cdot 2^{x^{2} - 2} x

Graph

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