derivative of 6^{6-x^2}

Lösung

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

- ln (6) \cdot 3^{6 - x^{2}} \cdot 2^{- x^{2} + 7} x

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

e^{(6 - x^{2}) l n (6)} (- 2 ln (6) x) : - ln (6) \cdot 3^{6 - x^{2}} \cdot 2^{- x^{2} + 7} x

= - ln (6) \cdot 3^{6 - x^{2}} \cdot 2^{- x^{2} + 7} x

d er i v a t i v e y = - 2 x + 7

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