derivative of 6^{x^2-3}

Lösung

\frac{d}{d x} (6^{x^{2} - 3})

ln (6) \cdot 3^{x^{2} - 3} \cdot 2^{x^{2} - 2} x

Schritte zur Lösung

\frac{d}{d x} (6^{x^{2} - 3})

Wende Exponentenregel an:

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

6^{x^{2} - 3} = e^{(x^{2} - 3) l n (6)}

= \frac{d}{d x} (e^{(x^{2} - 3) l n (6)})

Wende die Kettenregel an:

e^{(x^{2} - 3) l n (6)} \frac{d}{d x} ((x^{2} - 3) ln (6))

= e^{(x^{2} - 3) l n (6)} \frac{d}{d x} ((x^{2} - 3) ln (6))

\frac{d}{d x} ((x^{2} - 3) ln (6)) = 2 ln (6) x

= e^{(x^{2} - 3) l n (6)} \cdot 2 ln (6) x

Vereinfache

e^{(x^{2} - 3) l n (6)} \cdot 2 ln (6) x : ln (6) \cdot 3^{x^{2} - 3} \cdot 2^{x^{2} - 2} x

= ln (6) \cdot 3^{x^{2} - 3} \cdot 2^{x^{2} - 2} x