derivative of 6^{5x^4-10x^3+5}

Lösung

\frac{d}{d x} (6^{5 x^{4} - 10 x^{3} + 5})

ln (6) \cdot 6^{5 x^{4} - 10 x^{3} + 5} (20 x^{3} - 30 x^{2})

Schritte zur Lösung

\frac{d}{d x} (6^{5 x^{4} - 10 x^{3} + 5})

Wende Exponentenregel an:

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

6^{5 x^{4} - 10 x^{3} + 5} = e^{(5 x^{4} - 10 x^{3} + 5) l n (6)}

= \frac{d}{d x} (e^{(5 x^{4} - 10 x^{3} + 5) l n (6)})

Wende die Kettenregel an:

e^{(5 x^{4} - 10 x^{3} + 5) l n (6)} \frac{d}{d x} ((5 x^{4} - 10 x^{3} + 5) ln (6))

= e^{(5 x^{4} - 10 x^{3} + 5) l n (6)} \frac{d}{d x} ((5 x^{4} - 10 x^{3} + 5) ln (6))

\frac{d}{d x} ((5 x^{4} - 10 x^{3} + 5) ln (6)) = ln (6) (20 x^{3} - 30 x^{2})

= e^{(5 x^{4} - 10 x^{3} + 5) l n (6)} ln (6) (20 x^{3} - 30 x^{2})

e^{(5 x^{4} - 10 x^{3} + 5) l n (6)} = 6^{5 x^{4} - 10 x^{3} + 5}

= ln (6) \cdot 6^{5 x^{4} - 10 x^{3} + 5} (20 x^{3} - 30 x^{2})

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